Simple wealth distribution model causing inequality-induced crisis without external shocks

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns, or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent "$r>g$" (return rate $>$ growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the "water-divide" of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.Comment: 15 pages, 11 figures. Work initiated from discussion on Aristotle's status revisited by Paul Jorion in the many cases where the law of supply and demand fails. Accepted for publication in Physical Review E on April 19, 201

Milky Way and Andromeda past-encounters in different gravity models: the impact on the estimated Local Group mass

The Two-body problem of $M31$ and the Milky Way (MW) galaxies with a Cosmological Constant background is studied, with emphasis on the possibility that they experienced Past Encounters. By implementing the Timing Argument (TA), it is shown that if $M{31}$ and the MW have had more than one encounter then the deduced mass of the Local Group (LG) would be larger. Past encounters are possible only for non-zero transverse velocity, and their viability is subject to observations of the imprints of such near collisions. Using a recent $Gaia$ - based measurement of the transverse velocity we show that the presence of the Cosmological Constant requires the mass for the LG to be $35\%$ higher: $3.36^{+1.14}_{-0.70} \cdot 10^{12} M_{\odot}$ with no Cosmological Constant or $4.54^{+1.20}_{-0.75} \cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. If the LG has had one past encounter, the LG mass is $9.99^{+2.22}_{-1.58}\cdot 10^{12} M_{\odot}$ with a Cosmological Constant background. Modified Newtonian Dynamics (MOND) is studied as the accelerations of the Local Group are fully in the deep-MOND regime. MOND yields the order of magnitude for the expected baryonic mass only if at least one encounter occurred. While we only consider the LG as two point masses, our calculations provide a benchmark for future work with simulations to test Dynamical Friction and other effects. This model can be also used to test screening mechanisms and alternative theories of gravity.Comment: 16 pages. A revised versio

Radiation hydrodynamical models of the inner rim in protoplanetary disks

Many stars host planets orbiting within a few astronomical units (AU). The occurrence rate and distributions of masses and orbits vary greatly with the host stars mass. These close planets origins are a mystery that motivates investigating protoplanetary disks central regions. A key factor governing the conditions near the star is the silicate sublimation front, which largely determines where the starlight is absorbed, and which is often called the inner rim. We present the first radiation hydrodynamical modeling of the sublimation front in the disks around the young intermediate-mass stars called Herbig Ae stars. The models are axisymmetric, and include starlight heating, silicate grains sublimating and condensing to equilibrium at the local, time-dependent temperature and density, and accretion stresses parametrizing the results of MHD magneto-rotational turbulence models. The results compare well with radiation hydrostatic solutions, and prove to be dynamically stable. Passing the model disks into Monte Carlo radiative transfer calculations, we show that the models satisfy observational constraints on the inner rims location. A small optically-thin halo of hot dust naturally arises between the inner rim and the star. The inner rim has a substantial radial extent, corresponding to several disk scale heights. While the fronts overall position varies with the stellar luminosity, its radial extent depends on the mass accretion rate. A pressure maximum develops near the location of thermal ionization at temperatures about 1000 K. The pressure maximum is capable of halting solid pebbles radial drift and concentrating them in a zone where temperatures are sufficiently high for annealing to form crystalline silicates.Comment: accepted for Ap