New models are investigated in this paper, that describe equilibrium states of plates with Signorini type nonpenetration conditions. In these models, it is assumed that under appropriate loading, plates have special deformations with already known configurations of edges. For this case, we deal with new non-penetration conditions that allow us to describe more precisely the possibility of contact interaction of plate edges. Using the method of fictitious domains, it is proved that an original contact problem for a plate can be obtained by passing to the limit when a rigidity parameter tends to infinity from a family of auxiliary problems formulated in a wider domain. The mentioned family of problems model an equilibrium state of plates with a crack and depend on the positive rigidity parameter. For these problems, to prevent a mutual penetration of the opposite crack faces boundary conditions of inequality type are imposed on the inner boundary corresponding to the crack. For the problem, describing a plate with a crack that intersects the external boundary at zero angle (a case of a boundary having one cusp), the unique solvability is proved.

The paper considers equilibrium models of Kirchhoff-Love plates with rigid inclusions of two types. The first type of inclusion is described by three-dimensional sets, the second one corresponds to a cylindrical rigid inclusion, which is perpendicular to the plate’s median plane in the initial state. For both models, we suppose that there is a through crack along a fixed part of the inclusion’s boundary. On the crack non-penetration conditions are prescribed which correspond to a certain known configuration bending near the crack. The uniqueness solvability of a new problems for a Kirchhoff-Love plate with a flat rigid inclusion is proved. It is proved that when a thickness parameter tends to zero, the problem for a flat rigid inclusion can be represented as a limiting task for a family of variational problems concerning the inclusions of the first type. A solvability of an optimal control problem with a control given by the size of inclusions is proved

This article provides a detailed analysis of issues related to the complications while drilling in hydrate-bearing rocks of permafrost areas. The goal of the paper is to develop recommendations for preventing gas occurrence while drilling gas hydrate deposits and to eliminate gas leakiness of the intercasing space of the well. The results of modeling the effect of drilling mud injection on the temperature field of the well are presented. It is revealed that the most significant role is played by the injection rate of drilling mud and its temperature. The recommended flow rate of the process fluid should be within 0.30–0.45 m3/s, and its temperature should not exceed 20 °C. Controlling the parameters of drilling mud and its flow rate allows for avoiding intensive gas occurrence while drilling in gas hydrates. The presence of gas hydrates may be the cause of gas leakiness of the intercasing space in the permafrost area. One of the ways to eliminate leakiness is colmatation (clogging). A method of preventing leaks in the intercasing space of the gas well is the use of colmatating solution. An aqueous solution of sodium silicate with the addition of 2% polymer is used as a colmatating composition.

The spontaneous and magnetic-field-induced first-order magnetic phase transitions in single-crystal samples of the alloy system Mn2−xCrxSb (symmetry space group P4/nmm) are investigated in samples with x=0.06 and x=0.12. It is found that the spontaneous first-order transitions from the high-temperature to the low-temperature phase are not accompanied by complete vanishing of the magnetization. At the induced transitions the magnetization before and after the transition is an increasing linear function of field. It is concluded on the basis of the results that the ground state in these alloys cannot be one of collinear antiferromagnetism, as had been thought previously. Other possibilities for interpreting the ground state and the mechanisms of order–disorder transitions inherent to magnets with itinerant carriers of magnetism are examined. It is conjectured that the local magnetic moment has a ferromagnetic and a periodic component which are formed by itinerant d electrons and coexist in low- and high-temperature phases.