Time scale for the formation of the earth and planets and its role in their geochemical evolution

The initial mass of the solar nebula is discussed. Models of a massive nebula (two solar masses and more) encounter serious difficulties: an effective mechanism of transfer of the momentum from the central part of the nebula outward, capable of leading to formation of the sun and removal of half the mass of the nebula from the solar system has not been found. As a consequence of the instability of these models, their evolution can end with the formation, not a planetary system, but of a binary star. The possibility is demonstrated of obtaining acceptable growth rates for Uranus and Neptune by prolonging the thickening of preplanetary dust in the region of large masses. The important role of large bodies in the process of formation of the planets is noted. The impacts of such bodies, moving in heliocentric orbits, could have imparted considerable additional energy to the forming Moon, which, together with the energy given off by the joining of a small number of large protomoons, could have led to a high initial temperature of the moon

The rate of planet formation and the solar system's small bodies

The evolution of random velocities and the mass distribution of preplanetary body at the early stage of accumulation are currently under review. Arguments were presented for and against the view of an extremely rapid, runaway growth of the largest bodies at this stage with parameter values of Theta approximately greater than 10(exp 3). Difficulties are encountered assuming such a large Theta: (1) bodies of the Jovian zone penetrate the asteroid zone too late and do not have time to hinder the formation of a normal-sized planet in the asteroidal zone and thereby remove a significant portion of the mass of solid matter and (2) Uranus and Neptune cannot eject bodies from the solar system into the cometary cloud. Therefore, the values Theta less than 10(exp 2) appear to be preferable

Russian population ethnic structure: trends and transformations

Based on the census data from 1989, 2002 and 2010, the article analyzes the evolution of the ethnic structure of the population of the post-Soviet Russia from the territorial perspective. The stability of the ethnic structure of the "Russian mega nucleus" and indigenization of the national regions are considered in view of the differences in migration trends during the two inter-census periods and the socioeconomic situation in the regions. The urbanization rate of major ethnic groups is an indirect indicator of the prospects of traditional "primordial" ethnic identities in different ethnic groups. Special attention is paid to new trends - an increase in the number of people refraining from answering the question about their ethnic identity or giving an unclear answer. Alongside serious census errors, this phenomenon can be a result of growing complexity of the ethnic identity structures and the processes of modernization, which occur at different rates in Russian and national regions. Based on the 2010 census data, the article analyses the differences in polyethnicity between the rural and urban population, which are accounted for by the historical background, particularities of regional development, settlement features, and migration processes of the past two decades

Dynamical evolution of planetesimals in protoplanetary disks

The current picture of terrestrial planet formation relies heavily on our understanding of the dynamical evolution of planetesimals -- asteroid-like bodies thought to be planetary building blocks. In this study we investigate the growth of eccentricities and inclinations of planetesimals in spatially homogeneous protoplanetary disks using methods of kinetic theory. We explore disks with a realistic mass spectrum of planetesimals evolving in time, similar to that obtained in self-consistent simulations of planetesimal coagulation. We calculate the behavior of planetesimal random velocities as a function of the planetesimal mass spectrum both analytically and numerically; results obtained by the two approaches agree quite well. Scaling of random velocity with mass can always be represented as a combination of power laws corresponding to different velocity regimes (shear- or dispersion-dominated) of planetesimal gravitational interactions. For different mass spectra we calculate analytically the exponents and time dependent normalizations of these power laws, as well as the positions of the transition regions between different regimes. It is shown that random energy equipartition between different planetesimals can only be achieved in disks with very steep mass distributions (differential surface number density of planetesimals falling off steeper than m^{-4}), or in the runaway tails. In systems with shallow mass spectra (shallower than m^{-3}) random velocities of small planetesimals turn out to be independent of their masses. We also discuss the damping effects of inelastic collisions between planetesimals and of gas drag, and their importance in modifying planetesimal random velocities.Comment: 20 pages, 17 figures, 1 table, submitted to A

Two evolutional paths of an axisymmetric gravitational instability in the dust layer of a protoplanetary disk

Nonlinear numerical simulations are performed to investigate the density evolution in the dust layer of a protoplanetary disk due to the gravitational instability and dust settling toward the midplane. We assume the region where the radial pressure gradient at equilibrium is negligible so that the shear-induced instability is avoided, and also restrict to an axisymmetric perturbation as a first step of nonlinear numerical simulations of the gravitational instability. We find that there are two different evolutional paths of the gravitational instability depending on the nondimensional gas friction time, which is defined as the product of the gas friction time and the Keplerian angular velocity. If the nondimensional gas friction time is equal to 0.01, the gravitational instability grows faster than dust settling. On the other hand, if the nondimensional gas friction time is equal to 0.1, dust aggregates settle sufficiently before the gravitational instability grows. In the latter case, an approximate analytical calculation reveals that dust settling is faster than the growth of the gravitational instability regardless of the dust density at the midplane. Thus, the dust layer becomes extremely thin and may reach a few tenth of the material density of the dust before the gravitational instability grows.Comment: 4 pages, 3 figure

Iron oxide nanoparticles fabricated by electric explosion of wire: Focus on magnetic nanofluids

Nanoparticles of iron oxides (MNPs) were prepared using the electric explosion of wire technique (EEW). The main focus was on the fabrication of de-aggregated spherical nanoparticles with a narrow size distribution. According to XRD the major crystalline phase was magnetite with an average diameter of MNPs, depending on the fraction. Further separation of air-dry EEW nanoparticles was performed in aqueous suspensions. In order to provide the stability of magnetite suspension in water, we found the optimum concentration of the electrostatic stabilizer (sodium citrate and optimum pH level) based on zeta-potential measurements. The stable suspensions still contained a substantial fraction of aggregates which were disintegrated by the excessive ultrasound treatment. The separation of the large particles out of the suspension was performed by centrifuging. The structural features, magnetic properties and microwave absorption of MNPs and their aqueous solutions confirm that we were able to obtain an ensemble in which the magnetic contributions come from the spherical MNPs. The particle size distribution in fractionated samples was narrow and they showed a similar behaviour to that expected of the superparamagnetic ensemble. Maximum obtained concentration was as high as 5 % of magnetic material (by weight). Designed assembly of de-aggregated nanoparticles is an example of on-purpose developed magnetic nanofluid. Copyright © 2012 Author(s)

The angular momentum of two collided rarefied preplanetesimals and the formation of binaries

This paper studies the mean angular momentum associated with the collision of two celestial objects in the earliest stages of planet formation. Of primary concern is the scenario of two rarefied preplanetesimals (RPPs) in circular heliocentric orbits. The theoretical results are used to develop models of binary or multiple system formation from RPPs, and explain the observation that a greater fraction of binaries originated farther from the Sun. At the stage of RPPs, small-body satellites can form in two ways: a merger between RPPs can have two centers of contraction, or the formation of satellites from a disc around the primary or the secondary. Formation of the disc can be caused by that the angular momentum of the RPP formed by the merger is greater than the critical angular momentum for a solid body. One or several satellites of the primary (moving mainly in low-eccentricity orbits) can be formed from this disc at any separation less than the Hill radius. The first scenario can explain a system such as 2001 QW322 where the two components have similar masses but are separated by a great distance. In general, any values for the eccentricity and inclination of the mutual orbit are possible. Among discovered binaries, the observed angular momenta are smaller than the typical angular momenta expected for identical RPPs having the same total mass as the discovered binary and encountering each other in circular heliocentric orbits. This suggests that the population of RPPs underwent some contraction before mergers became common.Comment: 12 pages, Monthly Notices of Royal Astron. Society, in pres

Type I Planet Migration in Nearly Laminar Disks

We describe 2D hydrodynamic simulations of the migration of low-mass planets ($\leq 30 M_{\oplus}$) in nearly laminar disks (viscosity parameter $\alpha < 10^{-3}$) over timescales of several thousand orbit periods. We consider disk masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness parameters of $H/r = 0.035$ and 0.05, and a variety of $\alpha$ values and planet masses. Disk self-gravity is fully included. Previous analytic work has suggested that Type I planet migration can be halted in disks of sufficiently low turbulent viscosity, for $\alpha \sim 10^{-4}$. The halting is due to a feedback effect of breaking density waves that results in a slight mass redistribution and consequently an increased outward torque contribution. The simulations confirm the existence of a critical mass ($M_{cr} \sim 10 M_{\oplus}$) beyond which migration halts in nearly laminar disks. For \alpha \ga 10^{-3}, density feedback effects are washed out and Type I migration persists. The critical masses are in good agreement with the analytic model of Rafikov (2002). In addition, for \alpha \la 10^{-4} steep density gradients produce a vortex instability, resulting in a small time-varying eccentricity in the planet's orbit and a slight outward migration. Migration in nearly laminar disks may be sufficiently slow to reconcile the timescales of migration theory with those of giant planet formation in the core accretion model.Comment: 3 figures, accepted to ApJ

An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics

We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the standard WKB correction should be replaced by the solution to certain evolution equation.Comment: This is a preprint of an article whose final and definitive form has been published in Comm. Partial Differential Equations, available online at http://www.informaworld.co