Wealth distribution and collective knowledge. A Boltzmann approach

We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi, Toscani, J. Stat. Phys. 2005. The trades, which include both saving propensity and the risks of the market, are here modified in the risk and saving parameters, which now are assumed to depend on the personal degree of knowledge. The numerical simulations show that the presence of knowledge has the potential to produce a class of wealthy agents and to account for a larger proportion of wealth inequality.Comment: 21 pages, 10 figures. arXiv admin note: text overlap with arXiv:q-bio/0312018 by other author

On a kinetic model for a simple market economy

In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis.Econophysics;Boltzmann equation;wealth and income distributions;Fokker Planck model; Monte Carlo simulations; Pareto distribution

Hydrodynamic models of preference formation in multi-agent societies

In this paper, we discuss the passage to hydrodynamic equations for kinetic models of opinion formation. The considered kinetic models feature an opinion density depending on an additional microscopic variable, identified with the personal preference. This variable describes an opinion-driven polarisation process, leading finally to a choice among some possible options, as it happens e.g. in referendums or elections. Like in the kinetic theory of rarefied gases, the derivation of hydrodynamic equations is essentially based on the computation of the local equilibrium distribution of the opinions from the underlying kinetic model. Several numerical examples validate the resulting model, shedding light on the crucial role played by the distinction between opinion and preference formation on the choice processes in multi-agent societies.Comment: 30 pages, 15 figure

Boron isotope geochemistry of Na-bicarbonate, Na-chloride, and Ca-chloride waters from the Northern Apennine Foredeep basin: other pieces of the sedimentary basin puzzle

The boron stable isotope ratio δ11B of 12 water samples representative of three chemical facies (fresh Na-bicarbonate, brackish Na-chloride, saline, and brine Ca-chloride) has been analyzed. Interpretation of the δ11B data, along with the chemical compositions, reveals that Na-carbonate waters from the Northern Apennine are of meteoric origin, with boron contributions from clay desorption and mixing with seawater-derived fluids of Na-chloride or Ca-chloride compositions. The comparison of our new results with the literature data on other sedimentary basins of Mediterranean, and worldwide, confirms the contribution of Na-bicarbonate waters to the genesis of mud volcano fluids. The Na-chloride sample of Salvarola (SAL), which may represent the end-member of the mud volcanoes, and the Ca-chloride brine water from Salsomaggiore (SM) indicate boron release from clays compatible with the diagenetic process. The empirical equation: δ11B=[5.1364×ln(1/B)mgl-1]+44.601relating boron concentration and the stable isotope composition of the fluids observed in this study and the literature is proposed to trace the effect of diagenesis in sedimentary basins. A geothermometer associated to the diagenetic equation is also proposed: T{ring operator}C=[δ11B-38.873(±1.180)]/[-0.164(±0.012)] The application of this equation to obtain reservoir temperatures from δ11B compositions of waters should be carefully evaluated against the results obtained from other chemical and isotopic geothermometers from other basins around the world

The effects of pre-existing discontinuities on the surface expression of normal faults: insights from wet-clay analogue modeling

We use wet-clay analogue models to investigate how pre-existing discontinuities (i.e. structures inherited from previous tectonic phases) affect the evolution of a normal fault at the Earth\u2019s surface. To this end we first perform a series of three reference experiments driven by a 45\ub0 dipping master fault unaffected by pre-existing discontinuities to generate a mechanically isotropic learning set of models. We then replicate the xperiment six times introducing a 60\ub0-dipping precut in the clay cake, each time with a different attitude and orientation with respect to an initially-blind, 45\ub0-dipping, master normal fault. In all experiments the precut intersects the vertical projection of the master fault halfway between the center and the right-hand lateral tip. All other conditions are identical for all seven models. By comparing the results obtained from the mechanically isotropic experiments with results from experiments with precuts we find that the surface evolution of the normal fault varies depending on the precut orientation. In most cases the parameters of newly-forming faults are strongly influenced. The largest influence is exerted by synthetic and antithetic discontinuities trending respectively at 30\ub0 and 45\ub0 from the strike of the master fault, whereas a synthetic discontinuity at 60\ub0 and an antithetic discontinuity at 30\ub0 show moderate influence. Little influence is exerted by a synthetic discontinuity at 45\ub0 and an antithetic discontinuity at 60\ub0 from the strike of the master fault. We provide a ranking chart to assess fault-to-discontinuity interactions with respect to essential surface fault descriptors, such as segmentation, vertical-displacement profile, maximum displacement, and length, often used as proxies to infer fault properties at depth. Considering a single descriptor, the amount of deviation induced by different precuts varies from case to case in a rather unpredictable fashion. Multiple observables should be taken into consideration when analyzing normal faults evolving next to pre-existing discontinuities

Kinetic Modelling of Epidemic Dynamics: Social Contacts, Control with Uncertain Data, and Multiscale Spatial Dynamics

In this survey we report some recent results in the mathematical modelling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction between agents in which social characteristics play a key role in the spread of an epidemic, such as the age of individuals, the number of social contacts, and their economic wealth. Subsequently, for such models, we discuss the possibility of containing the epidemic through an appropriate optimal control formulation based on the policy maker’s perception of the progress of the epidemic. The role of uncertainty in the data is also discussed and addressed. Finally, the kinetic modelling is extended to spatially dependent settings using multiscale transport models that can characterize the impact of movement dynamics on epidemic advancement on both one-dimensional networks and realistic two-dimensional geographic settings

Multi-stage rodingitization of ophiolitic bodies from Northern Apennines (Italy): Constraints from petrography, geochemistry and thermodynamic modelling

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On a kinetic model for a simple market economy

In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of wealth among individuals. For this equation the stationary state can be easily derived and shows a Pareto power law tail. Numerical results confirm the previous analysis