Mathematical models describing the effects of different tax evasion behaviors

Microscopic models describing a whole of economic interactions in a closed society are considered. The presence of a tax system combined with a redistribution process is taken into account, as well as the occurrence of tax evasion. In particular, the existence is postulated, in relation to the level of evasion, of different individual taxpayer behaviors. The effects of the mentioned different behaviors on shape and features of the emerging income distribution profile are investigated qualitatively and quantitatively. Numerical solutions show that the Gini inequality index of the total population increases when the evasion level is higher, but does not depend significantly on the evasion spread. For fixed spread, the relative difference between the average incomes of the worst evaders and honest taxpayers increases approximately as a quadratic function of the evasion level.Comment: To appear in J. of Economic Interaction and Coordinatio

Hysteresis loops of magnetic thin films with perpendicular anisotropy

We model the magnetization of quasi two-dimensional systems with easy perpendicular (z-)axis anisotropy upon change of external magnetic field along z. The model is derived from the Landau-Lifshitz-Gilbert equation for magnetization evolution, written in closed form in terms of the z component of the magnetization only. The model includes--in addition to the external field--magnetic exchange, dipolar interactions and structural disorder. The phase diagram in the disorder/interaction strength plane is presented, and the different qualitative regimes are analyzed. The results compare very well with observed experimental hysteresis loops and spatial magnetization patterns, as for instance for the case of Co-Pt multilayers.Comment: 8 pages, 8 figure

The Bass diffusion model on finite Barabasi-Albert networks

Using a mean-field network formulation of the Bass innovation diffusion model and exact results by Fotouhi and Rabbat on the degree correlations of Barabasi-Albert networks, we compute the times of the diffusion peak and compare them with those on scale-free networks which have the same scale-free exponent but different assortativity properties. We compare our results with those obtained by Caldarelli et al. for the SIS epidemic model with the spectral method applied to adjacency matrices. It turns out that diffusion times on finite Barabasi-Albert networks are at a minimum. This may be due to a little-known property of these networks: although the value of the assortativity coefficient is close to zero, they look disassortative if one considers only a bounded range of degrees, including the smallest ones, and slightly assortative on the range of the higher degrees. We also find that if the trickle-down character of the diffusion process is enhanced by a larger initial stimulus on the hubs (via a inhomogeneous linear term in the Bass model), the relative difference between the diffusion times for BA networks and uncorrelated networks is even larger, reaching for instance the 34% in a typical case on a network with $10^4$ nodes.Comment: 19 pages, 8 figures. Misspelling in citations correcte

The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments

In 2002 a measurement of the effect of solar gravity upon the phase of coherent microwave beams passing near the Sun has been carried out with the Cassini mission, allowing a very accurate measurement of the PPN parameter $\gamma$. The data have been analyzed with NASA's Orbit Determination Program (ODP) in the Barycentric Celestial Reference System, in which the Sun moves around the centre of mass of the solar system with a velocity $v_\odot$ of about 10 m/sec; the question arises, what correction this implies for the predicted phase shift. After a review of the way the ODP works, we set the problem in the framework of Lorentz (and Galilean) transformations and evaluate the correction; it is several orders of magnitude below our experimental accuracy. We also discuss a recent paper \cite{kopeikin07}, which claims wrong and much larger corrections, and clarify the reasons for the discrepancy.Comment: Final version accepted by Classical and Quantum Gravity (8 Jan. 2008

Dynamic hysteresis from zigzag domain walls

We investigate dynamic hysteresis in ferromagnetic thin films with zigzag domain walls. We introduce a discrete model describing the motion of a wall in a disordered ferromagnet with in-plane magnetization, driven by an external magnetic field, considering the effects of dipolar interactions and anisotropy. We analyze the effects of external field frequency and temperature on the coercive field by Monte Carlo simulations, and find a good agreement with the experimental data reported in literature for Fe/GaAs films. This implies that dynamic hysteresis in this case can be explained by a single propagating domain wall model without invoking domain nucleation.Comment: 10 pages, 13 figures; minor modifications and two figures adde