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

Loss separation for dynamic hysteresis in magnetic thin films

We develop a theory for dynamic hysteresis in ferromagnetic thin films, on the basis of the phenomenological principle of loss separation. We observe that, remarkably, the theory of loss separation, originally derived for bulk metallic materials, is applicable to disordered magnetic systems under fairly general conditions regardless of the particular damping mechanism. We confirm our theory both by numerical simulations of a driven random--field Ising model, and by re--examining several experimental data reported in the literature on dynamic hysteresis in thin films. All the experiments examined and the simulations find a natural interpretation in terms of loss separation. The power losses dependence on the driving field rate predicted by our theory fits satisfactorily all the data in the entire frequency range, thus reconciling the apparent lack of universality observed in different materials.Comment: 4 pages, 6 figure

Power Spectral Density of Magnetization Dynamics Driven by a Jump-Noise Process

Random magnetization dynamics driven by a jump-noise process is reduced to stochastic magnetic energy dynamics on specific graphs using an averaging technique. An approach to analyzing stochastic energy dynamics on graphs is presented and applied to the calculation of power spectral density of random magnetization dynamics. An eigenvalue technique for computing the power spectral density under specific cases is also presented and illustrated by numerical results

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

Stochastic model of hysteresis

The methods of the probability theory have been used in order to build up a new model of hysteresis. It turns out that the reversal points of the control parameter (e. g., the magnetic field) are Markov points which determine the stochastic evolution of the process. It has been shown that the branches of the hysteresis loop are converging to fixed limit curves when the number of cyclic back-and-forth variations of the control parameter between two consecutive reversal points is large enough. This convergence to limit curves gives a clear explanation of the accommodation process. The accommodated minor loops show the return-point memory property but this property is obviously absent in the case of non-accommodated minor loops which are not congruent and generally not closed. In contrast to the traditional Preisach model the reversal point susceptibilities are non-zero finite values. The stochastic model can provide a good approximation of the Raylaigh quadratic law when the external parameter varies between two sufficiently small values.Comment: 13 pages, 14 figure

Hysteresis and noise in ferromagnetic materials with parallel domain walls

We investigate dynamic hysteresis and Barkhausen noise in ferromagnetic materials with a huge number of parallel and rigid Bloch domain walls. Considering a disordered ferromagnetic system with strong in-plane uniaxial anisotropy and in-plane magnetization driven by an external magnetic field, we calculate the equations of motion for a set of coupled domain walls, considering the effects of the long-range dipolar interactions and disorder. We derive analytically an expression for the magnetic susceptivity, related to the effective demagnetizing factor, and show that it has a logarithmic dependence on the number of domains. Next, we simulate the equations of motion and study the effect of the external field frequency and the disorder on the hysteresis and noise properties. The dynamic hysteresis is very well explained by means of the loss separation theory.Comment: 13 pages, 11 figure

Stochastic effects in a discretized kinetic model of economic exchange

Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker–Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data