The purpose of this survey is to describe invariants of cyclic coverings of graphs. The covered graph is assumed to be fixed, and the cyclic covering group has an arbitrarily large order. A classical example of such a covering is a circulant graph. It covers a one-vertex graph with a prescribed number of loops. More sophisticated objects representing the family of cyclic coverings include $I$-, $Y$-, and $H$-graphs, generalized Petersen graphs, sandwich-graphs, discrete tori, and many others. We present analytic formulae for counting rooted spanning forests and trees in cyclic coverings, establish their asymptotics, and study the arithmetic properties of these quantities. Moreover, in the case of circulant graphs we give exact formulae for computing the Kirchhoff index and present structural theorems for the Jacobians of such graphs. Bibliography: 95 titles.
In this work, the influence of the cluster formation process on the gas dynamics of a supersonic flow is studied by the method of electron-beam visualization. Corrections to the model for describing the transverse dimensions of supersonic flows under conditions of developed condensation are presented. Possible causes and conditions for the formation of a secondary cocurrent flow are analyzed. The influence of background gas penetration into the clastered flow has been studied. The conditions for the occurrence of an anomalous afterglow of a clastered flow upon initiation by an electron discharge are studied.
A review of the experimental work carried out on the vacuum gas-dynamic stands of the Applied Physics Department of the Novosibirsk State University is presented. Creation of these stands meeting the world’s requirements and equipped with modern diagnostic methods was based on the background experience from the Institute of Thermophysics of the Siberian Branch of the Russian Academy of Sciences under the guidance of A.K. Rebrov. A brief description of the stands and the results of some studies is given. Despite the limited possibilities of the university environment, the use of compact laboratory vacuum stands provides large-scale studies in various areas of rarefied gas dynamics.
Nozzle prototype for a diesel fuel reformer was investigated using numerical simulation. The main goal was to increase the rate and degree of fuel evaporation, as well as to improve the mixing characteristics between diesel fuel and superheated steam. A nozzle design was proposed with two internal regions, in which jets with opposite swirl directions were created. The simulation of mixing and evaporation of liquid fuel droplets and steam jets was performed in a finite volume formulation. The results of simulations show good uniformity of the mixture concentration downstream the nozzle exit, as well as high degree of evaporation, which is important for catalytic processes.
An abdominal aortic aneurysm (AAA) is a dangerous pathology that needs regular monitoring based on medical images. Currently, only visual estimates of the growth rate and methods based on the assessment of changes in the maximum diameter of the aneurysm in clinical practice are used. However, the quantitative assessment of vessel wall growth rate based on deformable image registration is gaining popularity in research. This paper presents a study of the applicability of the neural network approach of image registration for the quantitative growth assessment problem. In this study, we analyzed classical and neural network methods of image registration and used VoxelMorph and HyperMorph neural network architectures to evaluate local AAA growth based on the available dataset. Also, we compared the results of the obtained maximum local deformations of the AAA with the method of estimating the change in the maximum diameter.
The paper presents a study of the formation of gas hydrate in a colloidal solution of water + SDS + SiO 2 . The influence of sodium dodecyl sulfate (SDS) on the process of the kinetic promoter at various concentrations: 0, 100, 300, 500 ppm was studied. The process itself is described, the dependences of temperature and pressure changes on time for each case are presented. The conversions of gas and solution to the hydrate state are determined. Carbon dioxide was used as the hydrate-forming gas.
The results of a numerical study of a supersonic underexpanded jet flowing from a conical nozzle into a rarefied environment are presented. The modeling was performed by the direct simulation Monte Carlo method. The range of parameters corresponding to the expansion ratio 40 < n < 240, the hydrodynamic regime of the flow in the nozzle and the rarefied regime of interaction of the jet with the environment, characterized by Knudsen numbers in the range 0.03 < KnL < 0.2, is considered. It is shown that in the specified range of KnL a drastic rearrangement of the flow structure occurs. For the lower limit of the KnL range, a shock-wave structure typical of a highly underexpanded jet is observed. For Kn = 0.2, it completely degrades. Data have been obtained on the process of dimer formation in an expanding jet. An increase in the mole fraction of dimers with increasing distance from the nozzle throat is shown both in the conical nozzle and in the initial section of the jet expansion region.
An asymptotic new method of solving the generalized Boltzmann equation previously developed by the authors is presented, and its difference from the traditional Chapman-Enskog method is discussed. The application of this new method is considered by an example of an O2/O dissociating mixture flow with separation around a double cone. A comparison with available literature and experimental data is presented. The computed and measured surface heat fluxes are found to be in reasonable agreement. The computed surface heat flux is analyzed through comparisons to numerical results of other researchers and codes.
The validation of the computational LBM code FliudX3D is presented on the example of turbulent flow in a pipe at two Reynolds numbers: 5300 and 37700, built on the bulk velocity, pipe diameter and kinematic viscosity. Due to the LBM approach, the code performance allows massive calculations to be performed in a short period of time with a good agreement with the literature data for the lower Reynolds number. However, the lack of the possibility to refine the computational grid leads to insufficient resolution of the turbulent boundary layer for the higher Reynolds number.
Study of rivulet deflections and interactions on the surface of vertical flowing heated liquid film at Reynolds number Re = 75 and initial temperature T0 = 25oC has been carried out. For recognition of rivulets and calculation maximal deflection amplitude neural network YOLOv5 was used. Distribution of rivulets’ interaction is presented. Obtained results are in good agreement with the data for Re = 33.
A study of cavitating smooth hydrofoil and foil with a structural surface was carried out. The structural surface morphology was made by laser ablation technology with a step of 0.01 mm and wavelength of 1064 nm. High-speed visualization of cavitating hydrofoils at various of flow bulk velocity was performed. In the paper is presented a comparison of cavitation flow regimes for the smooth and the roughness hydrofoils at equal cavitation numbers. The maximal lengths of the attached cavities for different flow regimes are compared. The structural surface of hydrofoil allows delaying the nucleation of cavitation and reducing the attached cavity size at higher velocities of the incoming flow was obtained.
We have considered the option of generating cluster ions directly at the nozzle by initiating an electric discharge. Here, a low-temperature plasma in the flow is formed as a result of the outflow of a partially ionized gas. Conditions for the formation of clusters in the presence of excited particles are provided downstream. To implement this generation option, a scheme for creating an effective discharge in the diffuser part of a supersonic nozzle was proposed and implemented. The diagnostic system of the LEMPUS-2 gas-dynamic facility was adapted to register processes in a supersonic flow of ionized gas with clusters. Molecular nitrogen, which is weakly condensing under experimental conditions, was used as the primary reference gas. The methods of molecular beam mass spectrometry were used to study gas mixtures consisting of 20% methane in an inert carrier gas. Highly condensable argon and practically non-condensable helium were used as carrier gases. It was found that when using the ionized particle selection system for detection, only methane monomers and dimers are registered in mixtures with argon, whereas in mixtures with helium larger clusters are registered. A version of the explanation of the detected dependencies was presented.
Carbon black (soot) is a product obtained by thermal decomposition (pyrolysis) of hydrocarbons (usually oil) in a heat-carrier gas flow. Carbon black is widely used as a reinforcing component in the production of rubbers and plastics. Tires use 70% of all carbon produced. It is produced in a furnace, by injecting raw hydrocarbon with nozzles into the stream of combustion products of natural gas (called heat-carrier gas), a spray jet is will be formed, accompanied by evaporation of raw materials, and pyrolysis in the end. It is important that the raw material is completely evaporated before pyrolysis begins, otherwise coke will form, contaminating the product. To improve the technology of carbon production, in particular, to ensure the complete evaporation of raw materials before the start of pyrolysis, it is impossible to do without mathematical modeling of the process itself. It is the most important way to obtain the most complete and detailed information about the features of the reactor. Such phenomena are usually modeled using multiphase flows.
The external signs and conditions for the occurrence of sudden changes in the direction of ethanol micro-jets during vertical, from top to bottom, outflow from small-diameter capillaries into a rarefied medium (vacuum) are considered. A brief description of the equipment used, the organization of liquid preparation for the experiment, and the control of parameters are given. With the help of photo and video equipment, sudden transitions from dark areas of the jet to light ones and vice versa, stratification of the liquid jet into two, three or more fan streams, i.e. bifurcation. It is shown that with a decrease in the diameter of the capillary opening, the jet outflow is more stable, and the flow can retain its shape for a relatively long period of time. The process established by other researchers of the flow of liquid drops up the capillary has been confirmed. The reliability of the obtained results was verified by comparison with the known data by organizing the outflow from the same capillaries into the atmosphere.
Many scholars point to the crisis in the Russian bibliology. Meanwhile, those involved in the discussion specify the origins of the crisis in the discipline differently. One possible way to overcome the theoretical crisis of bibliology is to turn to Robert Darnton’s conceptual model of communications circuit. Robert Darnton is well known for his studies in the history of book culture of the modern era yet his model, which has long been recognized as a classic in international historical book studies, has been ignored by Russian bibliologists. The author describes the model that contemplates to identify agents of book communications; the sustained interactions between the agents structure and reproduce the world of book culture. The methodological context of the “pragmatic turn” that defines the model-based concept of book culture based on Clifford Geertz’s semiotic theory of culture, is revised. Possible ways of adapting Darnton’s model to the subsequent stages of media development are outlined. The communications circuit model offers research optics to consider book culture as the communicative wholeness within which the book serves as a medium to facilitate social interactions between different agents involved in the book communication process. Application of Darnton’s model would provide a new research agenda and its incorporation into the relevant international scholarly context.
Theoretical studies of the decomposition mechanism of energetic materials quite often scrutinize only the primary thermolysis reactions. However, the secondary reactions are crucial, inter alia, for proper building of the combustion models and understanding the autocatalytic processes. In the present study, we applied predictive DLPNO–CCSD(T) calculations to elucidate the kinetics and decomposition mechanism of a novel promising energetic material, 1,3,4,6-tetranitrooctahydroimidazo [4,5-d] imidazole (BCHMX). We identified eight previously unknown BCHMX conformers, both cis and trans in accordance to the spatial position of the H atoms bonded to a carbon bridge. Among them, the relative enthalpies of cis isomers lie in the narrow range ∼10 kJ mol–1 rendering them thermally accessible in the course of decomposition. The radical N–NO2 bond cleavage via one of the novel conformers is the dominant primary decomposition channel of BCHMX with the kinetic parameters Ea = 168.4 kJ mol–1 and log(A, s–1) = 18.5. We also resolved several contradictory assumptions on the mechanism and key intermediates of BCHMX thermolysis. To get a deeper understanding of the decomposition mechanism, we examined a series of unimolecular and bimolecular secondary channels of BCHMX. Among the former reactions, the C–C bond unzipping followed by another radical elimination of a nitro group is the most energetically favorable pathway with an activation barrier ∼113 kJ mol–1. However, contrary to the literature assumptions, the bimolecular H atom abstraction from a pristine BCHMX molecule by a primary nitramine radical product, not the nitro one, followed by another NO2 radical elimination, is the most important bimolecular secondary thermolysis reaction of BCHMX at lower temperatures. The isokinetic temperature of the bimolecular and unimolecular secondary reactions is ∼620 K. Unimolecular reactions might be important in dilute solutions, where bimolecular reactions are suppressed. The secondary reactions considered in the present work might be pertinent in the case of related energetic nitramines (e.g., RDX, HMX, and CL-20).
Based on the (differential) Encounter theory developed in the literature, which describes the change in the internal quantum states of particles encountered in liquid dilute solutions due to stochastic (diffusion) molecular motion, closed kinetic equations for the temporal change in the concentration of free radicals recombining at encounters were obtained. The recombination rates from singlet and triplet states are often different, the recombination products from these states may also be different, i.e., the recombination process is spin-selective. The radical spins experience any quantum spin interactions including Zeeman interaction with external magnetic fields and hyperfine couplings with magnetic nuclei and the processes of longitudinal and transverse spin relaxation. In general, recombination can occur both from singlet and triplet states. The rates of such recombination are not limited by the traditional contact model, implying that recombination occurs only at the radicals contact, and, like any spin interactions, are not assumed to be spherically symmetric. Under these general conditions, an unambiguous relationship has been established between the bulk recombination rate constant and the recombination yields of the corresponding geminate reaction from the singlet and triplet states. In the particular case of the same spatial dependence of the rates of singlet and triplet recombination, the rate constant can be expressed only through the singlet recombination yield for a singlet precursor or through the triplet recombination yield for a triplet precursor, despite the fact that recombination occurs from both spin states. The particular case of spherically symmetric recombination probability of the freely diffusing radical pairs in liquid solution, which is the most common one in the literature, is also considered.
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