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

Domain-wall coercivity in ferromagnetic systems with nonuniform local magnetic field

Domain-wall (DW) coercive field, H-CW, which characterizes pinning of DW's in soft magnetic materials, decreases strongly with increasing value of gradient, G, of the effective local DW-position-restoring magnetic field. Particular shapes of the dependence, H-CW(G), can be calculated from the mean energy dissipation of the DW moving over the particular profile of the DW pinning field, H-p. In this paper, H-CW(G) is calculated from a wall-pinning field, H-p, which is expressed as a stochastic function of the DW coordinate, x(DW). The wall-pinning field, H-p, is described as a Wiener-Levy stochastic process modified by two correlation lengths in such a way that H-p is stationary for large DW displacements and dH(p) /dx(DW) is well defined for small DW displacements. The computed H-CW(G) is close to a hyperbolic decrease, but it approaches finite values if G-->O and it decreases in a much steeper way than alpha 1/G for high values of G, which agrees with the experimental observations. Experimentally, the dependence H-CW(G) was measured on close-packed arrays of cylindrical bubble domains in two thin films of magnetic garnets, where the local field gradient, G, was controlled within the range 10(9)-10(10) A/m(2) by changing distances between neighboring DW's. The DW coercive field, H-CW, extrapolated from the measured values for G-->O was close to 80 A/m for both samples, while H-CW(G approximate to 10(10) A/m(2)) was several times smaller. Fitting the calculated H-CW(G) dependence to the experimental data, we obtained values of the Wiener-Levy correlation lengths well comparable to the DW width parameters

The predictability of the "Voyager" accident

International audienceOn 14 February 2005 a severe mistral storm caused substantial damage to the passenger cruiser "Voyager" between Balearic Islands and Sardinia. The storm had been well predicted. However, the ship was hit by one or more, apparently unexpected, large waves. Our aim was to understand if this was a freak event or it was within the expectable probability. At this aim we use our best estimate of the local wave conditions, obtained combining modelling and measured data. Starting from these we derive the probability of large waves, considering both linear and non-linear cases. Notwithstanding a correction towards the worse of the, otherwise inconsistent, available reports, on the basis of the data at disposal we conclude that, given the local conditions, the event was within the range of the potentially expectable wave heights. This turns out to be even more the case on the basis of recent results based on theoretical and experimental data

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

Network rewiring in the rr-KK plane

We generate correlated scale-free networks in the configuration model through a new rewiring algorithm which allows to tune the Newman assortativity coefficient $r$ and the average degree of the nearest neighbors $K$ (in the range $-1\le r \le 1$, $K\ge \langle k \rangle$). At each attempted rewiring step, local variations $\Delta r$ and $\Delta K$ are computed and then the step is accepted according to a standard Metropolis probability $\exp(\pm\Delta r/T)$, where $T$ is a variable temperature. We prove a general relation between $\Delta r$ and $\Delta K$, thus finding a connection between two variables which have very different definitions and topological meaning. We describe rewiring trajectories in the $r$-$K$ plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree ($k_{min} \ge 1$) which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbours in the branching approximation $\bar{z}_{2,B}$ is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored.Comment: 21 pages, 7 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