Melting and differentiation in Venus with a cold start: A mechanism of the thin crust formation

Recent works argue that the venusian crust is thin: less than 10-30 km. However, any convective model of Venus unavoidably predicts melting and a fast growth of the basaltic crust, up to its maximum thickness of about 70 km limited, by the gabbro-eclogite phase transition. The crust is highly buoyant due to both its composition and temperature and it is problematic to find a mechanism providing its effective recycling and thinning in the absence of plate tectonics. There are different ways to solve this contradiction. This study suggests that a thin crust can be produced during the entire evolution of Venus if Venus avoided giant impacts

The thermal conditions of Venus

Models of Venus' thermal evolution are examined. The following subject areas are covered: (1) modified approximation of parameterized convection; (2) description of the model; (3) numerical results and asymptotic solution of the MAPC equations; (4) magnetism and the thermal regime of the cores of Earth and Venus; and (5) the thermal regime of the Venusian crust

Kinetics of crystal growth in a terrestrial magma ocean

The problem of crystal sizes is one of the central problems of differentiation of a terrestrial magma ocean and it has been an arbitrary parameter in previous models. The crystal sizes are controlled by kinetics of nucleation and crystal growth in a convective magma ocean. In contrast with crystallization in magma chambers, volcanic lavas, dikes, and other relatively well studied systems, nucleation and crystallization of solid phases occur due to the adiabatic compression in downward moving magma (adiabatic “cooling”). This problem is solved analytically for an arbitrary crystal growth law, using the following assumptions: convection is not influenced by the kinetics, interface kinetics is the rate controlling mechanism of crystal growth, and the adiabatic cooling is sufficiently slow for the asymptotic solution to be valid. The problems of nucleation and crystal growth at constant heat flux from the system and at constant temperature drop rate are shown to be described with similar equations. This allows comparison with numerical and experimental data available for these cases. A good agreement was found. When, during the cooling, the temperature drops below the temperature of the expected solid phase appearance, the subsequent evolution consists of three basic periods: cooling without any nucleation and crystallization, a short time interval of nucleation and initial crystallization (relaxation to equilibrium), and slow crystallization due to crystal growth controlled by quasi-equilibrium cooling. In contrast to previously discussed problems, nucleation is not as important as the crystal growth rate function and the rate of cooling. The physics of this unusual behavior is that both the characteristic nucleation rate and the time interval during which the nucleation takes place are now controlled by a competition between the cooling and crystallization rates. A probable size range for the magma ocean is found to be 10^(−2) − 1 cm, which is close to the upper bound for the critical crystal size dividing fractional and nonfractional crystallization discussed elsewhere in this issue. Both the volatile content and pressure are important and can influence the estimate by 1–2 orders of magnitude. Different kinds of Ostwald ripening take place in the final stage of the crystal growth. If the surface nucleation is the rate-controlling mechanism of crystal growth at small supercooling, then the Ostwald ripening is negligibly slow. In the case of other mechanisms of crystal growth, the crystal radius can reach the critical value required to start the fractional crystallization. It can happen in the latest stages of the evolution when the crystals do not dissolve completely and the time for the ripening is large

Nonfractional Crystallization of a Terrestrial Magma Ocean

It has been suggested that evolution of a terrestrial magma ocean does not unavoidably follow a fractional crystallization scenario. Convection is able to preclude differentiation until a sharp viscosity increase occurs near some critical crystal fraction. However, this kind of crystallization and its physical and chemical consequences have not been previously studied. We consider an end-member, called here nonfractional crystallization. We begin with a simple equilibrium thermodynamical model of partial melts which is based on an ideal three-component phase diagram. It allows a self-consistent calculation of physical and chemical parameters in the melting range at all interesting pressures. In particular, adiabats of the convecting magma ocean are calculated. The sharp increase in the viscosity is supposed to occur near the maximum packing crystal fraction. However, almost independently of this value, convection occurs even in the highly viscous quasi-solid part of the magma ocean and it is strong enough to prevent differentiation in deep regions. A kind of compositional convection occurs due to the layered differentiation, although it is weaker than the thermal convection. Only a surface region undergoes an essential differentiation via melt expulsion by compaction. The thickness of this layer depends on the rheology of partial melts, critical crystal fraction, and crystal sizes but in any case the basal pressure hardly can exceed 5 – 10 GPa. Because of lower pressures in the Moon, the thickness of the differentiating layer is large and thus the entire lunar magma ocean could undergo a strong differentiation. Remelting due to the energy released by differentiation is crucial only for much deeper layers (possibly deeper than about 1000 km for the Earth). For the remaining shallow layer (p < 5 – 10 GPa) the predicted increase of the melt fraction is less than 40 % at the surface and decreases to zero at the bottom of the differentiating layer. Thus, the nonfractional crystallization is suggested to be a likely alternative to the fractional crystallization. The crucial and still poorly understood factors are suspension in convective layers, rheology of partial melts, crystal size, and surface conditions. The most pronounced chemical consequence of the nonfractional crystallization is an almost completely preserved undifferentiated lower mantle and possibly a significant undifferentiated part of the upper mantle. At all depths, in the beginning of differentiation not only the first liquidus solid phase but also subsequent phases have been partially crystallized. So, when the differentiation begins, it involves mixtures of phases. It is important for the remaining layer where differentiation is unavoidable: this layer does not have as strong differentiation of minor elements as in the case of fractional crystallization but it will still involve differentiation of major elements. Future geochemical calculations of this multiphase differentiation, considering both major and minor elements, could help to constrain the differentiation further

Low-degree mantle convection with strongly temperature- and depth-dependent viscosity in a three-dimensional spherical shell

A series of numerical simulations of thermal convection of Boussinesq fluid with infinite Prandtl number, with Rayleigh number $10^7$, and with the strongly temperature- and depth- dependent viscosity in a three-dimensional spherical shell is carried out to study the mantle convection of single-plate terrestrial planets like Venus or Mars without an Earth-like plate tectonics. The strongly temperature-dependent viscosity (the viscosity contrast across the shell is $\geq 10^5$) make the convection under stagnant-lid short-wavelength structures. Numerous, cylindrical upwelling plumes are developed because of the secondary downwelling plumes arising from the bottom of lid. This convection pattern is inconsistent with that inferred from the geodesic observation of the Venus or Mars. Additional effect of the stratified viscosity at the upper/lower mantle (the viscosity contrast is varied from 30 to 300) are investigated. It is found that the combination of the strongly temperature- and depth-dependent viscosity causes long-wavelength structures of convection in which the spherical harmonic degree $\ell$ is dominant at 1--4. The geoid anomaly calculated by the simulated convections shows a long-wavelength structure, which is compared with observations. The degree-one ($\ell = 1$) convection like the Martian mantle is realized in the wide range of viscosity contrast from 30 to 100 when the viscosity is continuously increased with depth at the lower mantle.Comment: 18 pages, 10 figure

Bifurcations in a convection problem with temperature-dependent viscosity

A convection problem with temperature-dependent viscosity in an infinite layer is presented. As described, this problem has important applications in mantle convection. The existence of a stationary bifurcation is proved together with a condition to obtain the critical parameters at which the bifurcation takes place. For a general dependence of viscosity with temperature a numerical strategy for the calculation of the critical bifurcation curves and the most unstable modes has been developed. For a exponential dependence of viscosity on temperature the numerical calculations have been done. Comparisons with the classical Rayleigh-B\'enard problem with constant viscosity indicate that the critical threshold decreases as the exponential rate parameter increases.Comment: 16 pages, 5 figure

Mechanisms and Geochemical Models of Core Formation

The formation of the Earth's core is a consequence of planetary accretion and processes in the Earth's interior. The mechanical process of planetary differentiation is likely to occur in large, if not global, magma oceans created by the collisions of planetary embryos. Metal-silicate segregation in magma oceans occurs rapidly and efficiently unlike grain scale percolation according to laboratory experiments and calculations. Geochemical models of the core formation process as planetary accretion proceeds are becoming increasingly realistic. Single stage and continuous core formation models have evolved into multi-stage models that are couple to the output of dynamical models of the giant impact phase of planet formation. The models that are most successful in matching the chemical composition of the Earth's mantle, based on experimentally-derived element partition coefficients, show that the temperature and pressure of metal-silicate equilibration must increase as a function of time and mass accreted and so must the oxygen fugacity of the equilibrating material. The latter can occur if silicon partitions into the core and through the late delivery of oxidized material. Coupled dynamical accretion and multi-stage core formation models predict the evolving mantle and core compositions of all the terrestrial planets simultaneously and also place strong constraints on the bulk compositions and oxidation states of primitive bodies in the protoplanetary disk.Comment: Accepted in Fischer, R., Terasaki, H. (eds), Deep Earth: Physics and Chemistry of the Lower Mantle and Core, AGU Monograp

Towards a Self Consistent Plate Mantle Model that Includes Elasticity: Simple Benchmarks and Application to Basic Modes of Convection

One of the difficulties with self consistent plate-mantle models capturing multiple physical features, such as elasticity, non-Newtonian flow properties, and temperature dependence, is that the individual behaviours cannot be considered in isolation. For instance, if a viscous mantle convection model is generalized naively to include hypo-elasticity, then problems based on Earth-like Rayleigh numbers exhibit almost insurmountable numerical stability issues due to spurious softening associated with the co-rotational stress terms. If a stress limiter is introduced in the form of a power law rheology or yield criterion these difficulties can be avoided. In this paper, a novel Eulerian finite element formulation for visco-elastic convection is presented and the implementation of the co-rotational stress terms is addressed. The salient dimensionless numbers of visco-elastic plastic flows such as Weissenberg, Deborah and Bingham numbers are discussed in a separate section in the context of Geodynamics. We present an Eulerian formulation for slow temperature dependent, visco-elastic-plastic flows. A consistent tangent (incremental) formulation of the governing equations is derived. Numerical and analytical solutions demonstrating the effect of visco-elasticity, co-rotational terms are first discussed for simplified benchmark problems. For flow around cylinders we identify parameter ranges of predominantly viscous and visco-plastic and transient behavior. The influence of locally high strain rates on the importance of elasticity and non-Newtonian effects is also discussed in this context. For the case of simple shear we investigate in detail the effect of different co-rotational stress rates and the effect of power law creep. The results show that the effect of the co-rotational terms is insignificant if realistic stress levels are considered (e.g. deviatoric invariant smaller than 1/10 of the shear modulus say). We also consider the basic convection modes of stagnant lid, episodic resurfacing and mobile lid convection as applicable to a cooling planet. The simulations show that elasticity does not have a significant effect on global parameters such as the Nusselt number and the qualitative nature of the basic convection pattern. Our simple benchmarks show, however, also that elasticity plays a significant role for instabilities on the local scale of an individual subduction zone

MODERN ADMINISTRATIVE AND LEGAL METHODS OF COMBATING CORRUPTION IN THE FEDERAL PENITENTIARY SERVICE OF RUSSIA

Introduction: One of the priorities of the Federal Penitentiary Service is the fight against corruption. In this regard, this scientific article examines the effectiveness of modern administrative and legal methods of combating corruption in the Federal Penitentiary Service (FSIN) of Russia. These methods, based on a strict legal framework, include legislative provisions, recruitment, training, internal controls and measures to increase transparency. The article provides examples demonstrating tangible results and evaluates their impact using quantitative and qualitative indicators. The main purpose of the study: to analyze modern administrative and legal methods of combating corruption in the Federal Penitentiary Service of Russia, as well as to consider their effectiveness and prospects for development in the Russian penal system. The issues under consideration: The article examines the forms and causes of corruption in the Russian penal system, as well as the problems of the effectiveness of anti-corruption methods in the Federal Penitentiary Service of Russia. Methods used: The methodological basis of the research was the general scientific dialectical method of cognition and methods of system analysis, and a special legal method (comparative legal). Conclusions: Based on the conducted research, problems have been identified and recommendations have been proposed to improve legislation, protect informants and form an ethical culture. The author concludes that the commitment of the Federal Penitentiary Service of the Russian Federation to these methods discussed in the article indicates progress towards the creation of a penitentiary system free from corruption and complies with the legal principles of justice, honesty and transparency