In this paper, we deal with two-dimensional cubic Dirac equations, appearing as an effective model in gapped honeycomb structures. We give a formal derivation starting from cubic Schrodinger equations and prove the existence of standing waves bifurcating from one band-edge of the linear spectrum.

The theory of excitons in two dimensional materials including graphene and transition metal dichalcogenides (TMD) is complicated, as there appears a screened interaction in equations. Such interaction can be represented as Keldysh potential. The exact solution does not seem to exist yet. The method of searching appropriate solutions to equations of quantum mechanics is believed to solve this problem by using Laplace transform of tempered distributions and Volterra equations. The method is to seek solution as a Laplace transform of some tempered distribution that satisfies the appropriate Laplace spectral equation which, under Laplace transform, gives us the initial equation. Due to Paly-Wigner-Schwarz theorem, the image functions behavior depends on the geometry of original one support. In addition, the homogenous Volterra equation does not have nontrivial continuous solution. These constraints together with the fact that the studied equations turn out to be Volterra equations of III kind lead to a method that seems to solve a wide class of quantum mechanics equations.

A model of kinks appearance in the lipid bilayer membrane of erythrocytes, which are responsible for gas molecule transport, in particular, oxygen, is proposed. It was shown that the kinks arise due to the simultaneous action of transverse and tensile longitudinal mechanical stresses compressing the membrane. This model explains the membrane’s permeability sharp increase for gases during an erythrocyte passage through the microcapillary network with the compressive transverse mechanical stresses sharply increasing in its membrane. It was found that the equation of kinks motion has a soliton solution, so that a kink-soliton is formed in the bilayer of the erythrocyte membrane. The developed model is consistent with the previously experimentally established fact that the native erythrocyte membranes in the bloodstream undergo a structural transition, when small changes in blood pH, hormone concentration, and temperature dramatically change the conformation of the biomembranes and its functions by changing the mechanical stress field in the biomembrane.

In this paper, we investigate the possibility of stable migration of charge carriers over long distances in DNA-like macromolecular structures in the form of an adiabatic soliton and derive the conditions for the formation of solitons. We find two types of soliton solutions: symmetric and antisymmetric. Comparing the energy of both types of soliton solutions with the energy of free extra charge, we find the region of the system parameters in which the soliton states are more energetically favorable than the states of quasi-free charges. At the same time, which of the two mentioned soliton solutions corresponds to an energetically favorable state depends on the ratio of the energy parameters of the molecular structure.

A theory of a domain wall creation and propagation is built on a linearized version of the transformed Landau-Lifshitz-Gilbert equation. The Lakshmanan–Nakamura stereo-graphic transform, after extra exponential transformation, and, next – linerization partially save information of the original nonlinearity that allows one to keep the domain wall dynamics, form and properties. For cylindrical-symmetric wire geometry, the conventional orthonormal Bessel basis, combined with projecting operators technique applied to subspaces of directed propagation of domain walls is constructed. The physically significant problems of the dynamics switching at points far and close from a wire ends are formulated and its solutions are presented in the frame of the Fourier method. Stationary solutions are found and the wall structure along the wire and propagation plots are drawn.

A sensitive laser registration of weak polarization-optical responses was used for the investigations of dilute magnetic nanofluids. Criteria for weak and strong signals for probing of sample by laser radiation with deep modulation of polarization were considered. The magneto-optical responses of a kerosene-based fluid with magnetite nanoparticles were investigated over a wide (five orders of magnitude) range of concentrations. Weak polarization responses for this nanofluid were observed at record low volume concentrations of nanoparticles up to 10⁻⁷.

We have examined non classical effect i.e. higher order single mode antibunching and intermodel antibunching and higher order sub-poissonian photon statistics (HOSPS) in fifth harmonic generation non linear optical process using short time interaction technique. We have found that nonclassical effects directly depend on number of photons prior to interaction with non linear medium. The higher the number of photons present prior to an interaction, the higher will be the nonclassicality in the system. It is additionally found that stoke mode doesn’t fulfill the condition of single mode antibunching and HOSPS in fifth harmonic generation process. To examine the optical nonlinearity of nanoparticles, there are significant research efforts concerning the estimation of higher order nonlinear susceptibility which can be utilized as a source for the generation of higher order harmonic generation nonlinear optical processes [19].

We present a simulation of Casimir field generation in the 1D cavity with moving walls and arbitrary variation of boundary conditions. We design a numerical scheme based on the finite element method and compare photon generation due to variation of the geometry of the cavity and due to perturbation of the boundary conditions.

The paper discusses the results of a research on physicochemical and biochemical properties of the Keplerate-type molybdenum-based nanocluster polyoxometalates (POMs), which show promise in the field of biomedicine as a means of targeted drug delivery, including the transport to immune privileged organs. POMs can be considered as components of releasing systems, including the long-acting ones with feedback (for controlling the drug active component release rate). POMs are promising drugs for the treatment of anemia. Also, the paper deals with the results of studies of POM effect on living systems at the molecular and cellular levels, at that of individual organs, and on the organism as a whole. The mechanism and kinetics of POM destruction and possibilities of stabilization, the oscillatory phenomena manifestation, the formation of POM conjugates with bioactive substances which can be released during the destruction of POM, with polymer components, and with indicator fluorescent dyes, as well as forecasts for further research, are considered.

In this paper we have analyzed the broadening of the levels of the energy spectrum of indium antimonide quantum dots with a change of sample temperature. The position of the levels was determined by processing normalized differential tunneling current-voltage characteristics using the “cubic” model of a quantum dot. Comparison of the calculated values of spectrum broadening with experimental results showed qualitative and quantitative agreement between the results. It is concluded that with a decrease in the quantum dot size and, accordingly, an increase in the energy gap ε_c1 − ε_v1, the broadening in percentage will decrease, which should lead to an increase in the temperature stability of the electrophysical parameters.

Ni₃Si₂O₅(OH)₄ phyllosilicate nanoscrolls were investigated by two techniques: the bending-based test method of AFM and the indentation method with visual control in STEM. In the first case, the average measured Young’s modulus, about 200 GPa, turned out to be significantly higher than in the second one, 40 GPa. The reasons for this discrepancy are analyzed.