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## Publications

Publications (33)

A necessary physical condition for steady-state mantle convection is the marginal stability of convective boundary layer (CBL) accommodating the transition from conductive lithosphere to convective mantle. We incorporate the marginal stability condition (MSC) of the CBL into the lithosphere thermal modeling using it instead of the heat flow boundar...

In the steady state, the convective boundary layer (CBL) (the transition from the lithosphere to the convecting mantle, the lithosphere-asthenosphere boundary) is on the verge of stability. This determines its depth, thickness, and the steady-state temperature distribution in the lithosphere. Had the mantle been homogeneous, the base of the lithosp...

Thermobarometry of xenolites/xenocrysts from 39 kimberlites of Eurasia, Africa, and North America demonstrates that the deepest xenolites, as well as all the other, are exhumed from the depleted lithosphere implying in agreement with petrologic and geochemical data that the kimberlite sources are situated within the limits of the depleted lithosphe...

Based upon the most complete modern plateau basalt, carbonatite and kimberlite databases, we show the existence of spatiotemporal correlations between these three types of intraplate magmatism. These correlations are evident everywhere in Eurasia and Africa but they are absent in North America. A probable cause of such correlations is an interactio...

High abundances of incompatible elements in kimberlites are indicative
of low or even infinitesimal melting degree in a source. This means that
initially protokimberlite melts exist as a system of dispersed small
inclusions while the kimberlite transportation to the surface assumes
formation of macroscopic melt pools. In other words, an inevitable...

For the problem of matrix compaction and melt segregation a general mush continuity equation is derived, which explicitly
expresses the coupling between the melt percolation and the inelastic matrix deformation and closes the governing equation
set. Besides, a general equation is obtained, which describes the change in the volume of pore space due...

Two-phase aggregates, a special case of which is partially molten systems, are commonly modelled as an interpenetrating flow of two viscous liquids and are therefore described in terms of the fluid mechanics. The governing equation set of fluid mechanics describing a two-phase aggregate is incomplete as it consists of nine equations (momentum and m...

Melting on a slipping fault interface has been considered one of the mechanisms capable of lowering the effective fault friction during rapid slip, although there is still debate about the magnitude and even the sign of the corresponding shear stress perturbation. Laboratory experiments conducted at high (order of m/s) slip velocities but low (orde...

Field observations of pseudotachylites and experimental studies of high-speed friction indicate that melting on a slipping interface may significantly affect the magnitude of shear stresses resisting slip. We investigate the effects of rock melting on the dynamic friction using theoretical models of shear heating that couple heat transfer, thermody...

1] Analysis of the trace element contents in kimberlites from various provinces around the world, including South Africa, India, and Yakutia (Siberia, Russia), reveals remarkable similarity of the maximum abundances. In addition, we find that abundances of the rare earth elements (REE) in the South African kimberlites are highly coherent between in...

The extreme enrichments of kimberlitic magmas in incompatible elements (e.g., compared to a typical undepleted mantle) are usually attributed to low degrees of melting and/or metasomatized source compositions. We present a model explaining the observed enrichment of kimberlitic magmas with rare earth elements (REE) in terms of melt migration throug...

A wide range of tectonic structures exists on the territory of the Ukraine. Observations of geomagnetic induction vectors revealed anomalously high conductivity of many of them. A quasi-3D geoelectrical model of the Earth's crust and upper mantle of the Ukraine is based upon a thin-sheet approximation inside a regional cross-section of the electric...

We consider deformation due to sill-like magma intrusions using a model of a horizontal circular crack in a semi-infinite elastic solid. We present exact expressions for vertical and horizontal displacements of the free surface of a half-space, and calculate surface displacements for a special case of a uniformly pressurized crack. We derive expres...

We investigate surface deformation associated with currently active crustal magma bodies in Socorro, New Mexico, and Long Valley, California, USA. We invert available geodetic data from these locations to constrain the overall geometry and dynamics of the inferred deformation sources at depth. Our best-fitting model for the Socorro magma body is a...

This paper presents numerical models of crystallisation and cooling of sill-like and cylindrical low-temperature intrusions, i.e. intrusions of magmas with crystallisation and intrusion temperatures not in excess of the temperature of melting of host rocks. The model takes into account the latent heat of crystallisation and convective heat transfer...

In part 1 of this article [1], a quantitative model was proposed of earth's surface deformation, which occurs due to magma ingress, under superlithostatic pressure, to form a sill-like crustal intrusion. The intrusion chamber was modeled by a circular horizontal crack in an elastic half-space. Integral Hankel transforms were applied to reduce the p...

Part 1 of this article discusses a quantitative model of deformation of the earth's surface by sill-type pressure. A horizontal, circular, fluid-filled crack in an elastic semi-space is con trusion. Integral Hankel transforms were used in order to reduce the problem of a stressed, crack-containing semi-space to a system of Fredholm equations of the...

The effect of high confining pressure on fluid‐filled crack growth is considered. Exact solutions are given for a two‐dimensional horizontal crack in an infinite elastic body using the approximation of Dugdale‐Barenblatt (DB) model. It is shown that for equilibrium cracks (i.e. for cracks on the verge of propagation) the large‐scale crack character...

This paper is concerned with the problem of crystallization of the phase-heterogeneous mantle and the interaction of this process with sedimentation. It is shown that for slow motion of phase-change boundaries the problem is reduced to solving a simple system of ordinary first-order differential equations. The motion is to be considered 'slow' if t...

A model for the origin of galactic cosmic rays is discussed, wherein most of the high-energy particles observed in the Galaxy would be accelerated during periods of activity in the galactic nucleus, recurring at intervals of 10â·â»â»Â¹Â°sup 8/ yr. The total energy of the cosmic rays accelerated during each active period would be 10âµâµâ»â»Â¹...

Many years ago physical and radio-astronomical arguments and data led to the assumption that cosmic rays in the Galaxy (and probably in other galaxies) fill a more or less extended halo, but are not concentrated in the disk. It was not so long ago, however, that the existence of a radio-halo was discovered, in which the effective dimensions increas...

X-ray observations indicate that the North Polar Spur (NPS) is the remnant of the explosion of some object. It is premature, however, to affirm with confidence that the explosion of a supernova led to its formation. The problem is that only the angular dimensions of the spur have been measured directly. In order to determine the fundamental charact...