In this study, we consider the time-symmetric initial data problem for GR minimally coupled with a phantom scalar field and a Maxwell field. The main focus is on initial data sets describing two interacting mouths of the same traversable wormhole. These data sets are similar in many respects to the Misner initial data with two black holes.

We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett. 93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and asymmetric couplings. Only the simplest of these waves are stable, which is confirmed by numerical simulations for a finite population. We demonstrate that for asymmetric coupling, a weakly turbulent traveling chimera regime is established, both from an initial standing chimera or an unstable traveling wave profile. The weakly turbulent chimera is a macroscopically chaotic state, with a well-defined synchronous domain and partial coherence in the disordered domain. We characterize it through the correlation function and the Lyapunov spectrum.

The paper concerns vector bundles on the projective line over the ring of integers. The bundles are of rank 2 with trivial generic fiber. Twistings of such a bundle of certain degree are considered. It is proved that for sufficiently high degrees, there exist nonvanishing sections of the corresponding twistings.

This article presents the results of examining pilot bainite steel railroad rails and their tests. It is shown that the set of properties typical of these rails is unreachable in standard perlite steel rails and includes a combination of high strength, hardness, ductility, and impact toughness. Bainite steel rails exhibit a better resistance to fatigue defect formation and a greater fracture toughness and, at the same time, increased contact-fatigue strength and reliability at low temperatures. Considering the demand for rails designed for use at high loads, complex track plan, and low temperatures on the railroads of the Eastern Testing Area and Northern Latitudinal Railway, bainite steel seems an expedient alloy for application.

Исследованы образцы титансодержащего шлака АО «ЕВРАЗ НТМК» от доменного передела железорудного концентрата уральских титаномагнетитовых руд Качканарского месторождения с целью изучения возможности извлечения титана. Исходные образцы отличаются способом кристаллизации. Один образец получен при послойном сливе шлака в траншею и охлаждении его водой (далее – шлаки с быстрой кристаллизацией), второй образец – шлаковые корки, оставшиеся в чаше после слива жидкой части (далее – шлаки с медленной кристаллизацией). Химический и фазовый составы всех исследованных образцов аналогичные, содержание TiO2 составляет ~10,5%. Основной фазой (матрицей) является акерманит-геленит, которая составляет ~65%. Титансодержащей фазой является перовскит ~26%. Шлаки с быстрой кристаллизацией характеризуются мелкой структурой титансодержащей фазы со средним размером частиц ~13 мкм. Титансодержащая фаза состоит на 88% из частиц площадью более 100 мкм2 со средним размером частиц ~17 мкм. Шлаки с медленной кристаллизацией характеризуются более крупной структурой титансодержащей фазы, размеры таких частиц ~30 мкм. Титансодержащая фаза состоит на 92% из крупных частиц площадью более 500 мкм2 со средним размером частиц ~40 мкм. Для механического обогащения предпочтительно использовать шлаки с медленной кристаллизацией, характеризующиеся крупными включениями титансодержащей фазы – перовскита. Размеры титансодержащей фазы и соотношение плотностей перовскита и акерманит-геленит (матрицы) на уровне 1,35 позволяют исследовать возможность механического выделения титансодержащего концентрата по плотности на концентрационном столе. The samples of the titanium-containing slag of EVRAZ NTMK JSC from the blast furnace process of concentrate of titanomagnetite ore the Ural Kachkanar deposit field in order to study the possibility of extracting titanium were investigated. The initial samples differ in crystallization method. One sample was obtained with a layer slag in a trench and cooling with water (hereinafter referred to as slags with fast crystallization), the second sample is slag crusts that remain in the cup after draining the liquid part (hereinafter referred to as the slags with slow crystallization). The chemical and phase compositions of all studied samples are similar the content of TiO2 is ~10.5%. The main phase (matrix) is akermanite-gehlenite, which is ~65%. The titanium-containing phase is perovskite ~26%. The fast crystallization slags are characterized by a fine structure of the titanium-containing phase with an average particle size of ~13 μm. The titaniumcontaining phase consists of 88% of particles of more than 100 μm2 with an average particle size of ~17 μm. A larger structure of the titanium-containing phase, the dimensions of such particles ~30 μm characterize the slow crystallization slags. The titaniumcontaining phase consists of 92% of large particles with an area of more than 500 μm2 with an average particle size of ~40 μm. For mechanical enrichment, it is preferable to use slags with slow crystallization, characterized by large inclusions of the titanium-containing phase - perovskite. The size of the titanium-containing phase and the ratio of perovskite density and akermanite-gehlenite (matrix) at the level of 1.35 make it possible to investigate the possibility of mechanical separation of the titanium-containing concentrate on the density on the concentrating table.

Using a differential aerosol spectrometer (DSA), a study was made of the homogeneous formation of solid phase nuclei in the process of laser-plasmochemical deposition of SiCN from hexamethyldisilazane vapor in a flow of plasma-forming argon gas. It was found that the characteristic size of SiCN nanoparticles in the gas phase is in the range of 20–120 nm and depends on the HMDS vapor concentration and the total argon flow rate. The studies performed have shown that the formation of a layer of silicon carbonitride in laser plasma-chemical deposition proceeds with the formation of nuclei in the gas phase, and upon their collision with the substrate and activation by laser plasma, it leads to the formation of a solid nanostructured coating.

We consider the features of the dynamics of the wave-packet self-action within the framework of a model described by the one-dimensional discrete nonlinear Schrödinger equation with allowance for the effects of acoustic relaxation of the nonlinear response of the medium. Such models are actively used to describe the energy transfer along protein molecules. Analytical and numerical studies show that the dynamics of the wave packets with energies exceeding the critical values significantly differs from the field evolution in a continuous medium. The behavior of initially smooth (on the scale of the distance between the structural elements of the medium) and initially localized field distributions propagating at subsonic speed is studied in detail. A specific self-action regime, which is not characteristic of the continuous limit, is shown to exist where the wave packet, during its propagation, slows down to a complete stop while undergoing self-compression to the size of the lattice period. Radiation losses increase significantly at the final stage of this process and eventually lead to the formation of a soliton-like structure, which usually moves in the opposite direction (with respect to the initial one). In the case of wave packets with supersonic initial speed, the self-action dynamics develops in a similar way. However, in this case, the motion of the quasisoliton which carries most of the energy becomes subsonic during the backward propagation. As applied to the molecular chains, the considered effects lead to a noticeable increase in the localized action of the compressed excitation on individual structural elements of the discrete medium.

Experimental studies of the NiCr powder interaction with the CO2-laser radiation in the conditions of free jets of a coaxial nozzle for laser cladding are carried out. Optical diagnostics is used with the video recording of moving particles and registration of the radiation spectrum. The influence of the type of working gas, i.e., air and argon, as well as laser operation modes - the continuous CW and pulse-periodic PP on plasma ignition - is studied. An increase in the average particle velocity from 3 m/s in a cold flow to 10 m/s, when exposed to a laser, was found and the maximum velocity values at the level of 50-60 m/s were registered. The phenomena of particle break-up and plasma plume formation on their surface are described. It is shown that particles rotating with a frequency of 30-40 kHz are present in the powder flow. The continuous thermal radiation of particles and the spectral lines of plasma radiation in the range of 400-900 nm are analyzed.

We analyze the synchronization dynamics of the thermodynamically large systems of globally coupled phase oscillators under Cauchy noise forcings with a bimodal distribution of frequencies and asymmetry between two distribution components. The systems with the Cauchy noise admit the application of the Ott-Antonsen ansatz, which has allowed us to study analytically synchronization transitions both in the symmetric and asymmetric cases. The dynamics and the transitions between various synchronous and asynchronous regimes are shown to be very sensitive to the asymmetry degree, whereas the scenario of the symmetry breaking is universal and does not depend on the particular way to introduce asymmetry, be it the unequal populations of modes in a bimodal distribution, the phase delay of the Kuramoto-Sakaguchi model, the different values of the coupling constants, or the unequal noise levels in two modes. In particular, we found that even small asymmetry may stabilize the stationary partially synchronized state, and this may happen even for an arbitrarily large frequency difference between two distribution modes (oscillator subgroups). This effect also results in the new type of bistability between two stationary partially synchronized states: one with a large level of global synchronization and synchronization parity between two subgroups and another with lower synchronization where the one subgroup is dominant, having a higher internal (subgroup) synchronization level and enforcing its oscillation frequency on the second subgroup. For the four asymmetry types, the critical values of asymmetry parameters were found analytically above which the bistability between incoherent and partially synchronized states is no longer possible.

Kummer’s tower is a family of number fields obtained by taking all possible roots of a rational base. The goal of the paper is to present several series of units in the towers with the bases two and three.

An assessment of the possibility of steel direct microalloying with cerium was performed using thermodynamic modeling of cerium reduction from slags of CaO– SiO2– Ce2O3 system containing 15 % Al2O3 and 8 % МgO, additional additives of reducing agents (aluminum or ferrosilicoaluminium), at temperatures of 1550 and 1650 °C using the HSC 6.1 Chemistry (Outokumpu) software package. Depending on the additional additives of aluminum or ferroglycoaluminium, metal temperature, slag basicity and content of cerium oxide, 0.228 to 40.5 ppm of cerium transfers into the metal. With an additional additive of aluminum from slag (Y1) containing 1.0 % of cerium oxide, 0.228 ppm of cerium is transferred to the metal at 1550 °C. An increase in the system temperature to 1650 °C is accompanied by a slight increase in cerium content, reaching no more than 0.323 ppm. When added to ferrosilicoaluminium metal, cerium content in the metal is higher and amounts to 0.402 and 0.566 ppm at 1550 and 1650 °C, respectively. When concentration of cerium oxide in the slag (Y2) increases to 7.0 %, more signifcant increase in cerium content in the metal is observed, reaching in temperature range of 1550 – 1650 °C, 1.65 – 2.31 ppm with aluminum additives and 2.90 – 4.05 ppm with ferrosilicoaluminium additives. The most noticeable increase in cerium content in the metal is observed with an increase in slag basicity. During formation of slags with basicity of 2 – 3, containing 1 – 7 % Ce2O3, the equilibrium concentration of cerium in the metal varies from 0.5 to 4 ppm with aluminum additives and 1 – 7 ppm with ferro­silicoaluminium additives at 1550 °C. Slags transfer to the increased (up to 3 – 5) basicity is accompanied by an increase in the equilibrium content of cerium in the metal to 4 – 12 ppm with aluminum additives and 7 – 20 ppm with ferrosilicoaluminium additives at Ce2O3 content of 3 – 7 % and, as a result, an increase in efciency of cerium reduction process.

Specific features of the self-action of wave fields are studied in the framework of a discrete nonlinear Schrödinger equation (DNSE). It is shown analytically and numerically that the dynamics of wave packets with initially normal group-velocity dispersion in systems described by this model equation may differ significantly from the evolution of similar distributions in a continuous medium. The behavior of wave fields with initially smooth (compared to the lattice period) amplitude profile and phase front is analyzed in detail, and the mechanism of their destruction in chains of equidistant elements is studied. A modification of the dispersionless approximation is proposed, which makes it possible to theoretically describe the effects leading to the development of small-scale instabilities against the background of a smooth envelope and to its subsequent significant deformations (up to destruction). Estimates of critical parameters are presented above which one should expect the above-mentioned processes (uncharacteristic of continuous media).

The paper studies modules over a certain generalized ring. This ring is the noncommutative tensor square of the ring of integers. The modules in question are related to some interesting arithmetic problems. In particular, they are related to the solved Gauss class-number problem for imaginary quadratic fields.

The paper concerns vector bundles on the projective line over the ring of integers. The bundles are of rank 2 and are obtained by change of a certain base. The source bundle runs over the bundles with trivial generic fiber and simple jumps. The minimal degree of nondegenerate sections of bundles in question is calculated. Certain interesting phenomena are discovered.

The article describes theoretical and experimental studies of dependence of viscosity, coefficients of sulfur and boron distribution between slag and metal, and wear degree of periclase-carbon refractories on basicity and boron oxide content in slag. It is shown that formed slags have basicity of 2.0 – 5.0 and rather high liquid mobility. These slags are characterized by an equilibrium interfacial distribution coefficient of sulfur increased to 5 – 20, which provides equilibrium sulfur content in the metal reduced to 0.001 – 0.005 %. The results of fundamental studies of the physicochemical properties of refining slags of СаО – SiO2 – В2O3 – Al2O3 – MgO system formed the basis for development of the composition of environmentally friendly fluorine-free ladle slags and technological methods for their formation in ladle-furnace unit. The recommended composition of such slags of low viscosity, which allows deep metal desulfurization, direct steel microalloying with boron and low aggressive effect on periclase-carbon refractories, provides formation of slags with a basicity of 3.0 – 4.0, containing 1 – 4 % B2O3 , 15 % Al2O3 and 8 % MgO. The formation of environmentally friendly ladle slags of the recommended composition was carried out in a ladle-furnace by loading lime, boron-containing material – colemanite (Turkey) containing 39 – 41 % B2O3 , 26 – 28 % CaO, not more than 5 % SiO2 and 3 % MgO, and pyramidal aluminum into the steel-teeming ladle for slag deoxidation and boron recovery. Introduction of the developed technology for the formation of ladle slags of recommended composition ensured the production of economically alloyed low-carbon structural boron-containing steels with a low sulfur content, incl. for large diameter pipes with high strength properties.

We consider a one-dimensional oscillatory medium with a coupling through a diffusive linear field. In the limit of fast diffusion this setup reduces to the classical Kuramoto-Battogtokh model. We demonstrate that for a finite diffusion stable chimera solitons, namely localized synchronous domain in an infinite asynchronous environment, are possible. The solitons are stable also for finite density of oscillators, but in this case they sway with a nearly constant speed. This finite-density-induced motility disappears in the continuum limit, as the velocity of the solitons is inverse proportional to the density. A long-wave instability of the homogeneous asynchronous state causes soliton turbulence, which appears as a sequence of soliton mergings and creations. As the instability of the asynchronous state becomes stronger, this turbulence develops into a spatio-temporal intermittency.

We consider an ensemble of identical phase oscillators coupled through a common diffusion field. Using the Ott–Antonsen reduction, we develop dynamical equations for the complex local order parameter and the mean field. The regions of the existence and stability are determined for the totally synchronous, partially synchronous, and asynchronous spatially homogeneous states. A procedure of searching for inhomogeneous states as periodic trajectories of an auxiliary system of the ordinary differential equations is demonstrated. A scenario of emergence of chimera structures from homogeneous synchronous solutions is described.

We study the quantum properties of light propagating through an array of coupled nonlinear waveguides and forming a discrete soliton. We demonstrate that it is possible to use certain types of quasi-solitons to form continuous variables entanglement between the certain pair of waveguides. Moreover, there is a possibility to entangle several pairs of waveguides independently. We show that the entanglement is generated for arbitrary high intensity of the input laser field, so it does not require a special material with an extremely high nonlinearity coefficient. Also, absorption in the waveguide media does not influence the discussed process too much.

We consider an array of nonlocally coupled oscillators on a ring, which for equally spaced units possesses a Kuramoto-Battogtokh chimera regime and a synchronous state. We demonstrate that disorder in oscillators positions leads to a transition from the synchronous to the chimera state. For a static (quenched) disorder we find that the probability of synchrony survival depends on the number of particles, from nearly zero at small populations to one in the thermodynamic limit. Furthermore, we demonstrate how the synchrony gets destroyed for randomly (ballistically or diffusively) moving oscillators. We show that, depending on the number of oscillators, there are different scalings of the transition time with this number and the velocity of the units.

Physicochemical characteristics of the nitrogen-alloyed steel melt of the 04Kh20N6G11M2AFB grade (nitrogen content 0.47–0.49%) are investigated by using the torsional vibration method of a crucible with metal in the atmosphere, which provides a stable nitrogen content during the experiment (80% nitrogen and 20% helium). Using the method sensitivity to the aggregate state of the tested substance, at a heating rate of 0.0033–0.0050 K/s, the liquidus temperatures are experimentally determined for the 04Kh20N6G11M2AFB steel (1660–1666 K) and low nitrogen steel ([N] = 0.063%) with the identical content of other elements (1685–1690 K). These results make it possible to recommend the value of the coefficient –60 K/% [N] for the calculated assessment of nitrogen influence on the liquidus temperature of complex and high alloy steels. The viscosity of the 04Kh20N6G11M2AFB steel melt is relatively high ((11.5 ± 0.7) ×10–7 m2/s) in comparison with the traditional austenitic steels ((8.2 ± 0.2) × 10–7 m2/s) with a relatively small partial effect of nitrogen. A significant nonequilibrium of the structural state of the 04Kh20N6G11M2AFB steel melt is revealed by the high-temperature viscometry methods. The comparative analysis of polytherms and kinematic viscosity isotherms of the 04Kh20N6G11M2AFB steel melt and its low nitrogen ([N] = 0.063%) analogue makes it possible to conclude that the nitrogen presence in concentrations close to saturation plays a decisive role in the melt nonequilibrium level and low relaxation rate. This is confirmed by the results of special experiments on saturation with nitrogen of low nitrogen steel, in which a sharp increase in nonequilibrium of the melt structural state is recorded when nitrogen concentration in metal reaches the limiting values (0.45–0.50%). There is a potential possibility to increase and stabilize the operational properties of corrosion resistant nitrogen-alloyed steels due to reducing the melt’s structural state nonequilibrium by excluding the excess of limiting values of nitrogen concentrations for the chemical composition considered.