The main results of research by laboratory staff

• Problems about the dynamics of nonlinear localized deformations in a two-dimensional graphene lattice, a mass-in-mass metamaterial lattice, and others have been solved. Model nonlinear equations are derived, the analysis of which makes it possible to predict the deformation-strength properties of materials with a complex internal structure.
• New model nonlinear partial differential equations are asymptotically derived to describe dynamic processes in materials with a complex internal structure. An asymptotic approach has been developed that makes it possible to obtain the continuum limits of models of lattices of materials with an internal structure in the wavelength ranges of different wavelengths.
• New analytical and numerical solutions are constructed for localized strain waves described by two-dimensional nonlinear partial differential equations. the constructed solutions make it possible to establish the conditions for the localization of nonlinear deformations with the parameters of the internal structure of the material.
• Feedback control methods have been developed that make it possible to achieve the required shape and speed of a nonlinear localized wave in a number of systems that describe dynamic processes in media with a complex internal structure. Physical methods are found for implementing these control mechanisms, in particular, by means of boundary conditions for stresses on the side surface of the waveguide. For one of the models of a metamaterial, a control method has been developed that makes it possible to carry out the passage of a deformation wave through the band gap.
• A nonlinear model of deformation of crystalline media with a complex lattice has been developed. In the nonlinear model, the deformation of the medium is described by the acoustic mode vector and the optical mode vector. The nonlinear model in a high stress field describes a radical rearrangement of the crystal lattice, the formation of a superlattice, phase transformations of the martensitic type, the appearance of various types of defects (micropores, microcracks, microseals, main cracks, dislocations, etc.), a decrease in the activation energy of structural rearrangement processes depending on external influences and parameters of the crystalline medium. These physical and mechanical processes are implemented in modern technologies for obtaining new materials with an internal structure and are not described by the classical linear model, in which the displacements of lattice atoms are assumed to be small, not going beyond the crystal cell.
• Mathematical methods have been developed for solving particular boundary value problems that model individual processes of medium deformation in the field of high external influences. The developed analytical approaches and the obtained exact solutions of nonlinear partial differential equations are of independent importance for the development of the theory of nonlinear equations of mathematical physics.
• The developed mathematical implementation of the nonlinear model makes it possible to use it both for describing modern technologies for obtaining new materials and for the processes of their targeted application.
• The possibility of superfluidity of simple liquids in carbon nanotubes is shown. Until now, it was believed that this phenomenon is possible in the so-called quantum liquids, for example 4He, at ultralow temperatures.
• Computer simulation of the behavior of active nematics in closed two-dimensional nanoscopic regions gave results qualitatively close to those observed experimentally.
• Models have been developed and numerically solved that describe biochemical processes in the human body and blood vessels, propagation of localized waves in crystalline media. The video shows an illustration of the propagation of a localized energy pulse through a scalar harmonic crystal lattice.
• It is shown that two hydrogen flux peaks correspond to one given hydrogen activation energy in the hydrogen diffusion model, if we take into account the features of hydrogen accumulation in metals during artificial hydrogenation, namely, the formation of a thin layer with a high hydrogen content at the sample boundary. The number of peaks in the hydrogen flow is fundamental in determining the activation energy by the thermodesobion method. Based on Kissinger's calculations, it is generally accepted that for each dependence of the peak temperature on the heating temperature, there corresponds a linear dependence in the coordinates of the Chu-Li diagram. It is shown by analytical calculations in the case of a one-dimensional case and numerical calculations in the case of a 3-dimensional body that a thin layer of high hydrogen concentration near the sample boundary gives an additional peak with a nonlinear dependence, and also that at high heating rates, the dependence for the extraction of internal hydrogen also becomes non-linear .