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Analytical methods are used to study nonlinear deformation of a plane with an elliptical inclusion. The elastic properties of a material of the plane and inclusion are described with a semi-linear material. The external load is constant nominal (Piola) stresses at infinity. At the inclusion boundary, the conditions of the continuity for stresses and displacements are satisfied. Semi-linear material belongs to the class of harmonic, the methods of the theory of functions of a complex variable are applicable to solving nonlinear plane problems. Stresses and displacements are expressed in terms of two analytical functions of a complex variable, determined by the boundary conditions on the inclusion contour. It is assumed that the stress state of an inclusion is uniform (the tensor of nominal stresses is constant). This hypothesis made it possible to reduce the difficult nonlinear problem of conjugation of two elastic bodies to the solution of two more simpler problems for a plane with an elliptical hole. The validity of this hypothesis is justified by the fact that the constructed solution exactly satisfies all the equations and boundary conditions of the problem. The same hypothesis was used earlier by other authors to solve linear and nonlinear problems of an elliptical inclusion. In the article, a comparative analysis of the stresses and strains is carried out for two models of harmonic materials — semi-linear and John’s. Various variants of values of elasticity parameters of the inclusion and matrix have been considered.

Accurate and controlled movement of small, untethered objects within soft tissues has many potential applications in medical robotics. While medium reaction forces due to slow movement of solid objects in viscoelastic fluids are well-known, such forces have received much less attention in soft media and tissues where the movement is accompanied by highly non-linear and history dependent phenomena. This paper develops a model of such forces for spherical solids. The reaction forces are investigated experimentally in the limit when the spherical solid moves at only a small fraction of its diameter per second. A mathematical model consistent with observations is proposed. The key element of the model is the history-dependent nature of the medium reaction force. A method of the model parameter identification is described, and its experimental implementation is demonstrated in gels that simulate soft tissues. In the experiments, known magnetic forces are employed as the external forces to drag a permanent magnet sphere inside Agarose gel phantom, and video tracking assisted by template matching calculations is used to accurately track the sphere translation. Numerical simulations of the model illustrate results that are consistent with observations.

The process of removal of heavy metal ions as part of the multi-component system from electrolyte solutions by means of electroflotation and filtration with presence of the high-molecular compounds (HMC) of different nature has been studied. Studies were performed in solutions with ions of iron (III), nickel (II), copper (II), lead (II) and zinc(II), as well as NaCl and Na2SO4 (pH 9.5–10.5). It has been shown that addition of the sulphate and sodium chloride mixture in 50 g/L concentration to solutions containing metal ions with total 0.1 g/L concentration reduced the absolute value of dispersed phase ζ-potential from −2.5 mV to −6 mV. The dispersed phase size is getting smaller, two particle types appear in the solution − 54 µm (72% of the total particle quantity) and 5.0 µm (28%). Rise of the total metal ion concentration up to 0.2 g/L results in reduction of the dispersed phase size: 1.5 µm (63%) and 46 µm (37%) particles prevail, the ζ-potential is reduced slightly (-7.1 mV). In this case, the rate of removal of the studied metals by mean of electroflotation is not more than 32–46%. Addition of the anionic HMS (flocculants and surfactants) to the solutions with the total concentration of metal ions of 0.2 g/L and salts of 50 g/L results in rise of dispersed phase ζ-potential and tends its value to the isoelectric point (±0 mV). When the cationic surfactants are added, the particle surface is recharged, the ζ-potential acquires the + values (5.3–7.8 mV). It has been concluded, that the rate of electroflotation removal of heavy metals from concentrated electrolyte solutions with the anionic HMS runs to 98–99% for all components. Subsequent solution filtration with the anionic flocculant allows for reduction of the residual concentration to the following values: 0.5∙10-4 g/L for Fe (III), Cu (II) and Pb (II) ions and. 0.1∙10-4 g/L for for Ni (II), 0.14∙10-3 g/L for Zn (II). Addition of the cationic, non-ionic and amphoteric surfactants does not result in increase of electroflotation process efficiency.

During the period of economic instability, the role of social support for vulnerable people growth. Among the measures aimed to fulfilling the social functions of the state, a special place is occupied by fiscal instruments, such as tax incentives. The article analyzes the foreign experience in the provision of social tax benefits on the example of Germany, Britain, France and the United States. The analysis allows to distinguish two basic directions of tax incentives aimed to provide social support: incentives aimed at persons engaged in social support (individuals and organizations, including charities) and aimed to those in need of social support.The analysis compares the Russian experience, makes recommendations on applications in Russia foreign experience.

Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (проект № 16-31-00065).

We have previously shown that Reactive Oxygen species and charges in atmospheric pressure nanosecond pulsed dielectric barrier discharges (nspDBD) stimulate immune function both in vitro and in vivoto enhance their migration, produce cytokines and kill tumor cells. (1–3) The immune cells act as “transport mechanism” for tumor killing effect of plasma so that deep tumors that are not directly accessible to plasma are also resolved. (4) Tumor growth is controlled not by plasma directly but by the action of plasma-activated immune cells. (4) Cells of the immune system also play an important role at all stages of wound healing. In the acute phase control of infection and inflammation is important. Their contribution in the late stages involves reepithelialization and angiogenesis to accelerate healing and reduce scar formation. (5, 6) Several studies suggest that plasma also benefits the process of wound healing. (7) However, the contribution of immune cells in plasma-mediated wound healing has not been studied. In this study we used the in vitro scratch assay to study if plasma improves wound healing through interaction with immune cells. In addition, the effect of bacterial infection on the healing process by plasma was examined. The implications of plasma stimulation of immune function for deep wound healing will be discussed.

The problems of elasticity for composite materials with inclusions have a great practical significance for physics, mechanics and other fields of science. In this paper the exact analytical solution to nonlinear problem of plane with elliptic inclusion is obtained. The constant nominal (Piola) stresses are given at infinity. Mechanical properties of plane and inclusion are modeling by harmonic semi-linear material. The stresses and displacements are expressed through two analytic functions of a complex variable, which are defined from nonlinear boundary conditions. Acceptance of a hypothesis, that nominal stress tensor is constant inside inclusion, has allowed to reduce a difficult problem of interface of two elastic bodies to the solution of two more simple problems for a plane with an elliptic hole. Validity of this hypothesis is proved to that obtained solution precisely satisfies to all equations and boundary conditions of a problem. The nominal hoop stresses were calculated on an interface of plane and inclusion for different material parameters.

The problems of elasticity for composite materials with holes and inclusions have a great practical significance for mechanics, physics and other areas of science. In this work the analytic solution of a plane problem (plane strain and plane stress) for bi-material plate with an elliptic hole is obtained. A hole is located entirely in a lower half-plane. The constant stresses are given at infinity and on the boundary of the hole an external load is applied. The methods of Kolosov–Muskhelishvili complex potentials, conformal mapping and superposition are used for the solution of the problem. The affinity of a hole to an interface makes essential influence on value of stresses in a vicinity of a hole and on value of stresses at an interface. For engineering applications it is important to know the fields of the stresses and displacements in order to estimate influence of a hole on strength of structure. From considered problems as special cases follow the solutions of problems about a half-plane with an elliptic hole, about an inclined crack in a bi-material plane and half-plane.

The singular plane problems of nonlinear elasticity (plane strain) are considered for bi-material infinite plane of John’s harmonic material. Using model of harmonic material has allowed to apply the theory of complex potentials and to obtain exact analytical global solutions of nonlinear problems. Among them it is problem of bi-material plate with the stresses and strains jumps on the interface. As an application of the problem of jumps, the problem of concentrated force on an interface boundary of two half-planes and the problem of interface crack. Mechanical properties of half-planes are described by the model of John’s harmonic material. Application of this model has allowed to use the methods of a complex functions theory and to obtain exact analytical solution of problems. The values of nominal stresses and displacements are founded. The asymptotic expansions based on the global solutions are constructed for stresses and displacements in a vicinity of a point force and in a vicinity of crack tip. As an example the case of a free crack in plate subjected to constant stresses at infinity is studied.

Problems of elasticity for composite materials with holes, cracks and inclusions have a great practical significance for mechanics, physics and other fields of science. The plane problem (plane strain or plane stress) for bi-material plate with elliptic hole is considered. On the boundary of the hole an external load is applied. At infinity constant stresses are given. The proximity of the hole to interface renders essential influence on the magnitude of stresses near the hole and on the interface. For engineering applications it is important to know fields of stresses and displacements. The method of Kolosov-Muskhelishvili complex potentials and the method of superposition are used for the solution of the problem. As a special case of the considered problem the solution of problem of an elliptic hole in a halfplane is represented.