Vol 51, No 6 (2017)

Regions of maximum shear and tension–compression stresses in the Martian interior have been revealed using two types of models: the elastic model and the model with an elastic lithosphere of varied thickness (150–500 km) positioned on a weak layer that has partially lost its elastic properties. The weakening is simulated by a ten-fold lower value of the shear modulus down to the core boundary. The numerical simulation applies Green’s functions (load number method) with the step of 1 × 1 grade along latitude and longitude down to a depth of 1000 km. The boundary condition is the expansion of the latest data on Martian topography and the gravitational field (model MRO120D) in spherical harmonics up to the degree and order of 90 in relation to the reference surface that is assumed an equilibrium spheroid. The considered two-level compensation model assumes nonequilibrium relief and density anomalies at the crust–mantle boundary to be the sources of the anomalous gravitational field. Calculations are performed for two test models of Martian internal structure with the crust mean thicknesses of 50 to 100 km and mean density of 2900 kg/m³. Considerable tangential and simultaneously compressive stresses occur under the Tharsis region. The main regions of high shear and simultaneously extentional stresses are located in the Hellas region crust and in the lithosphere of the following regions: Argyre Planitia, Mare Acidalium, Arcadia Planitia and Valles Marineris. The zone of high maximum shear and extentional stresses has been found at the base of the lithosphere under the Olympus volcano and that under the Elysium rise.

Radial contraction of the dust layer in the midplane of a gas–dust protoplanetary disk that consists of large dust aggregates is modeled. Sizes of aggregates vary from centimeters to meters assuming the monodispersion of the layer. The highly nonlinear continuity equation for the solid phase of the dust layer is solved numerically. The purpose of the study is to identify the conditions under which the solid matter is accumulated in the layer, which contributes to the formation of planetesimals as a result of gravitational instability of the dust phase of the layer. We consider the collective interaction of the layer with the surrounding gas of the protoplanetary disk: shear stresses act on the gas in the dust layer that has a higher orbital velocity than the gas outside the layer, this leads to a loss of angular momentum and a radial drift of the layer. The stress magnitude is determined by the turbulent viscosity, which is represented as the sum of the α-viscosity associated with global turbulence in the disk and the viscosity associated with turbulence that is localized in a thin equatorial region comprising the dust layer and is caused by the Kelvin–Helmholtz instability. The evaporation of water ice and the continuity of the mass flux of the nonvolatile component on the ice line is also taken into account. It is shown that the accumulation of solid matter on either side of the ice line and in other regions of the disk is determined primarily by the ratio of the radii of dust aggregates on either side of the ice line. If after the ice evaporation the sizes (or density) of dust aggregates decrease by an order of magnitude or more, the density of the solid phase of the layer’s matter in the annular zone adjacent to the ice line from the inside increases sharply. If, however, the sizes of the aggregates on the inner side of the ice line are only a few times smaller than behind the ice line, then in the same zone there is a deficit of mass at the place of the modern asteroid belt. We have obtained constraints on the parameters at which the layer compaction is possible: the global turbulence viscosity parameter (α < 10⁻⁵), the initial radial distribution of the surface density of the dust layer, and the distribution of the gas surface density in the disk. Restrictions on the surface density depend on the size of dust aggregates. It is shown that the timescale of radial contraction of a dust layer consisting of meter-sized bodies is two orders of magnitude and that of decimeter ones, an order of magnitude greater than the timescale of the radial drift of individual particles if there is no dust layer.