The magnetic Schr¨ odinger operator was studied on a figure 8-shaped graph. It is shown that for specially chosen vertex conditions, the spectrum of the magnetic operator is independent of the flux through one of the loops, provided the flux through the other loop is zero. Topological reasons for this effect are explained.

In this work, the storage of pure CO₂ and CH₄ gases and separation of their binary mixture in new type of nanostructured materials called boron imidazolate frameworks (BIFs) have been investigated using atomistic simulation to provide information for material selection in adsorbent designs. Adsorption isotherms and adsorption selectivities were computed using grand canonical Monte Carlo (GCMC). Our results showed that BIFs exhibit signi cantly higher selectivities for separation of CO₂ from CH₄ compared to other widely studied metal organic framework (MOF) materials.

The results of experimental studies for the formation kinetics of an intermetallic compound in the diffusion of gallium in copper are discussed. The mathematical model for the experimental study made it possible to calculate the diffusion coefficient of gallium in copper. A mathematical model for the kinetics of intermetallic compound formation at the reactive diffusion of gallium in a copper particle allows one to estimate the solidification time for diffusion-curing paste-based solder consisting of molten gallium and copper powder.

Metamaterials are artificial electromagnetic media that are structured on the subwavelength scale. Such structures were initially suggested for achieving the negative index of refraction, but later they became a paradigm for engineering electromagnetic space and controlling propagation of waves through the transformation optics and optically-induced magnetic response. The research agenda is now shifting towards tunable, switchable, nonlinear and sensing functionalities of metamaterials and their applications, and it involves the fields of metasurfaces and metadevices, with the recent demonstrations of breakthrough results with light-controlled metamaterials, nonlinear metamaterials, and tunable metasurfaces for MRI applications. Here, we briefly discuss the basic concepts of this rapidly growing research field, highlighting the recent developments in the physics of metamaterials, subwavelength nanophotonics, and graphene-based photonics.

We propose to treat the lowest bound states near the Abrikosov vortex core in type-II superconductors on the basis of the self-adjoint extension of the Hamiltonian of Aharonov-Bohm type with the localized magnetic flux. It is shown that the Hamiltonian for the excitations near the vortex core can be treated in terms of the generalized zero-range potential method when the magnetic field penetration depth δ is much greater than the coherence length ξ i.e. in the limit κ = δ/ξ ≫ 1. In addition, it is shown that in this limit it is the singular behavior of d∆/dr| _r=0 and not the details of the order parameter ∆(r) profile that is important. In support of the proposed model, we reproduce the spectrum of the Caroli-de Gennes-Matricon states and provide direct comparison with the numerical calculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921 (1998)]. In contrast to the empirical formula for the energy of the ground state in Hayashi, N. we use no fitting parameter. The parameters for the boundary conditions are determined in a self-consistent manner with Caroli-de Gennes-Matricon formula.

In this work, the modes of synthesizing copper nanoparticles for use in an optical initiation system were proposed. The optimal sizes of the copper particles in the pentaerythritol tetranitrate were estimated, for use as a cup of the optical detonator on the rst and the second harmonics of the Nd:Yag laser. For the rst harmonic of the Nd:Yag, laser the absorptivity maximum was 0.097 and the particles radius was 98 nm, for the second harmonic, the absorptivity maximum rose more than in 34 times, and it was equal to 3.29 and the copper particles radius was 30 nm. Comparison of the calculated critical energy densities shows that pentaerythritol tetranitrate, which contains the copper nanoparticles, must be signi cantly more sensitive ( 29 times) to the second harmonic than to the rst. The modes of synthesis for copper nanoparticles of the required size were determined and tested.

The problem of adequately describing transport processes of fluids in confined conditions is solved using methods of nonequilibrium statistical mechanics. The ‘fluid–channel wall’ system is regarded as a two-fluid medium, in which each phase has a particular velocity and temperature. The obtained results show that the transport equations in confined spaces should contain not only the stress tensor and the heat flux vector, but also the interfacial forces responsible for the transfer of momentum and heat due to the interaction with the wall surfaces. The stress tensor and the heat flux vector fluid can be expressed in terms of the effective viscosity and thermal conductivity. However, the constitutive relations contain additive terms that correspond to fluid–surface interactions. Thus, not only do the fluid transport coefficients in nanochannels differ from the bulk transport coefficients, but they are also not only determined by the parameters of the fluid.

Synthetic graphene oxide, in the form of graphene oxide paper (GOpp), and its reduction product– thermally exfoliated reduced graphene oxide (TErGO)– were studied by elastic and inelastic neutron scattering at low and room temperature conditions. The neutron diffraction patterns were analyzed to confirm stacking structures of both species consisting of 4– 6 and 8 layers of microsize lateral dimension and the interlayer distances of 7.21 Å and 3.36 Å, respectively. The one-phonon hydrogen amplitude-weighted density of vibrational states G( ) represents the inelastic incoherent neutron scattering spectra of the products. The study has revealed the retained water in the freshly made GOpp, corresponding to the lowest humidity. The analysis of the TErGO G( ) spectrum has disclosed the chemical composition of its circumference attributing the latter to sets of CH units with a minor presence of atomic oxygen.

The adsorption of hydrogen in carbon adsorbents was investigated at low and high temperatures (20.33, 77, 200 and 300 K) over a wide range of pressures using the classical density functional theory. The adsorbent was simulated by a slit-like pore presented by the gap between two monocarbon (graphene) walls. In most cases, our results demonstrate a good agreement with the available experimental and theoretical results of other authors. A conclusion was made that, contrary to the low temperature region (T<100 K), at high temperatures (200 and 300 K), predicted values for the adsorption and of the gravimetric density of hydrogen are not sufficient for the practical design of a hydrogen accumulator.

Silver nanoparticles (AgNPs) were synthesized in solutions of native and soluble starches in DMSO for the first time. The starches acted as reducing and stabilizing agents simultaneously. The kinetics of the process and its activation energy were determined by using UV-vis spectroscopy. The DMSO solution of soluble starch was characterized by better reductive activity than the native starch solution. The morphology and dispersion characteristics of AgNPs sols were evaluated from transmission electron microscopy (TEM). Sols, including spherical particles with mean diameter (D_m) 42.8 nm and metal rod-like particles, were obtained by using the native starch solution. Morphologically uniform sols of spherical AgNPs with D_m=37.2 nm were formed in the soluble starch solution. On the basis of zeta potential measurements, it was shown that the stability of a AgNPs dispersion in the soluble starch solution was higher in comparison to the native starch solution.

The model of microrelief formation on the surface of polymers was formulated, describing the connection between the microrelief structural elements distribution function on the states with the kinetics of macro molecule formation, aggregation and aggregates integration into the polymer body. Methods for calculating the kinetics of these processes, using experimental data on the microrelief properties, were developed. The developed methods have proven e ective in the study of microrelief on lms obtained by the evaporation of o xylene and toluene solutions of polystyrene, as well as polystyrene granulesmicrorelief. The hierarchical structures were found on the surface of these bodies, from which it was possible to extract information about the polymerization and aggregation of the polystyrene macromolecules. The obtained data are sum marized in the form of a morphological memory representation of the polymer bodies, consisting in the long-term preservation of nonequilibrium structures available for study without destroying the body, as well as the possibility to use the results of the study to describe the kinetics of these structures formation.

The e ects of variable compositions of manganese (IV) oxide- lead (II) oxide and manganese (IV) oxide vanadium (V) oxide on the GaAs thermal oxidation process have been studied. The spatial separation of the oxides in MnO2 + PbO and MnO2 + V2O5 binary compositions activating the thermal oxidation of GaAs has made it possible to locate the interactions between these oxides that are responsible for the non-linear e ects observed in their coaction. Solid-phase interactions enhance the chemostimulating activities of both oxides (a positive nonlinear e ect takes place). Gas-phase interactions cause a marked negative deviation from the additive chemical stimulation e ect.

The investigation of concentration dependence of mass transport properties (diffusion coefficients and viscosity) of the water soluble light fullerene tris-malonate– C₆₀[=C(COOH)₂]₃ in aqueous solutions was provided. Activation energies for the diffusion and viscous current were calculated.

A theory for forming Ir-atomic nanoclusters in a dielectric matrix of Na₄Ir₃O₈ structure and spinel-like structures is suggested. The atomic order in the Na₄Ir₃O₈ structure is investigated by group-theoretical methods of phase transition theory. The critical irreducible representation τ , generating appearance of enantiomorphic P4₁32 (P4₃32)-phases from high symmetry spinel-like phase with space group Fd3m, is six dimensional irreducible representation k₁₀(τ₁) (in Kovalev designation). Ir and Na atoms form an intriguing atom ordering, giving rise to a network of corner shared Ir triangles, called a hyperkagome lattice. It is shown that inside the hyperkagome lattice, there are closed metal contours of chemical bonds formed by Ir-clusters – decagons. Unusual physical properties of solid solutions on the basis of Na₄Ir₃O₈ are expected. The existence of hyperkagome lattices in six types in ordered spinel structures is theoretically predicted.