Phase Diagram of Metal-Insulator Transition in System with Anderson-Hubbard Centers

The model of a strongly correlated system in which periodically spaced Anderson-Hubbard centers are introduced into narrow-band metal is considered. Besides the interactions between localized magnetic moments and strong on-site Coulomb interaction, the model takes into account the hybridization of localized and band states. To study the efect of the lattice deformation on the electrical properties of the system the phonon term and elastic energy have been taken into account. Green functions for band and localized electrons have been found. On this base, the energy spectrum has been investigated as function of model parameters, temperature and external pressure. The criterion of metal-insulator transition for integer value of electron concentration has been derived and the phase diagram of the metal-insulator transition has been built.Comment: presented at 12 International Simposium on Physics of Materials, Prague 4-8.09.201

Research of strengthening process of machines details surfaces by treatment spark digits

Розраховано математичне сподівання площі зміцненої поверхні деталі шляхом обробки імпульсами одиничних іскрових розрядів, яке залежить від кількості розрядів та їх площі. Досліджено залежність частки зміцненої поверхні від кількості імпульсів розряду при різних значеннях їх площі та від величини площі одиничного розряду при дії різною кількістю розрядів. Аналіз отриманих результатів свідчить про необхідність урахування площі одиничного іскрового розряду та їх кількості при розробленні технології зміцнення деталей машин.The mathematical hope of area of the fixed detail surface is calculated by treatment of high spark bits impulses, which depends on the amount of digits and their area. Dependence of part of the fixed surface is investigational on the amount of impulses of digit at the different values of their area and from the size of area of high bit at the action of digits a different amount. An analysis of investigated results testifies to the necessity of account of area of high bit and their amount at development of technology of strengthening of details of machines

Mathematical modelling of the process of pipeline deformation through which gas-liquid mixtures with aggressive components are transported

Purpose Mathematical modelling of the process of deformation of pipeline, transporting gas-liquid mixtures with aggressive components and a comparative analysis of the value of the specified velocity depending on the dynamic viscosity of the multicomponent gas mixture is conducted. Design/methodology/approach A mathematical model of the process of leakage of the transported product due to the loss of tightness of the pipe based on the system of Navier-Stokes equations with boundary conditions with considering the geometry of the leakage zones and the value of the leakage rate is implemented. Findings Models of the process of deformation of the pipeline due to displacements of a certain set of surface points by specifying different types of functions, describing the geometry of deformed sections are constructed. The method of calculating the tensely deformed state based on the data on the movement of surface points by comparing different ways of setting functions, taking into account the actual configuration of sections and axes is improved. The change of flow characteristics in the pipeline when changing the structure of the mix, transported by studying of influence of change of dynamic viscosity is investigated; The method of calculating the rate of leakage of the mixture in case of loss of tightness due to the occurrence of critical stresses in the pipe material is improved. Research limitations/implications Building a model of the deformation process, information about the nature, duration of forces and loads affecting the pipeline is not used. The law of the pipeline movement was constructed having taken into account the deformation of the sections in three directions. The necessity to take wind loads into account, estimating the real tensely deformed state was displayed. Practical implications Using the method of calculating the tensely deformed state based on the data on the movement of surface points by comparing different ways of setting functions, taking into account the actual configuration of sections and axes. Originality/value According to the computational algorithms created on the basis of the specified models, the calculations of the tense state of the pipelines and the flow rate of the mixture depending on its composition were performed. An analysis of the results of calculations - tense intensity and flow rate depending on the dynamic viscosity of the mixture is performed. The influence on the flow parameters - the flow rate of the mixture and the force of hydraulic resistance - changes in the dynamic viscosity of the mixture is analyzed