New Objects in Scattering Theory with Symmetries

We consider 1D quantum scattering problem for a Hamiltonian with symmetries. We show that the proper treatment of symmetries in the spirit of homological algebra leads to new objects, generalizing the well known T- and K-matrices. Homological treatment implies that old objects and new ones are be combined in a differential. This differential arises from homotopy transfer of induced interaction and symmetries on solutions of free equations of motion. Therefore, old and new objects satisfy remarkable quadratic equations. We construct an explicit example in SUSY QM on $S^1$ demonstrating nontriviality of the above relation

The Numerical Simulation of Shallow Water: Estimation of the Roughness Coefficient on the Flood Stage

The results of the numerical simulations of the dynamics of shallow waters for Volga-Akhtuba Floodplain are discussed. The mathematical model is based on the system of Saint-Venant equations. Numerical solution applies a combined Lagrangian-Eulerian (cSPH-TVD) algorithm. We have investigated the features of the spring flood in 2011 and found the inapplicability of the hydrodynamical model with the constant roughness coefficient n M . We have found a good agreement between the results of numerical simulations and the observational data at gauging stations which allows us to estimate n M in low water n M min = 0.02 and the maximum water level in the river Volga n M max = 0.06–0.07

TRANSIENT PROCESSES IN ELECTRICAL COMPLEX OF PRODUCTION WELL WITH DOWNHOLE COMPENSATOR OF REACTIVE POWER

Link for citation: Glazyrin A.S., Isaev Yu.N., Kopyrin V.A., Timoshkin V.V., Kladiev S.N., Khamitov R.N., Kovalev V.Z., Losev A.F., Leonov A.P., Popov  E.I. Transient processes in electrical complex of production well with downhole compensator of reactive power. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 5, рр.168-180. In Rus. The relevance. At the present time at routine complication of technological processes to increase efficiency of production processes due to introduction of new equipment conflicts between functional capabilities of various technical means and their ability to function with specified quality, in specified electromagnetic environment and do not create inadmissible electromagnetic interference to other technical means. The electrical engineering complex for oil production includes a combination of ground and submersible electrical equipment assembled for receiving, transforming electrical energy, controlling its flow, converting electrical energy into mechanical energy and transmitting it to a submersible pump, including various electrical and electronic devices: a control station with a frequency converter, a step-up transformer, a cable line, a submersible electric motor, a downhole reactive power compensator and other devices. Any change in the layout of electrical systems for extracting oil or technical characteristics of the equipment used requires careful analysis of transient processes between the operating modes of electrical equipment in order to prevent the risks of false triggering of electrical equipment protection devices. The purpose: analysis of transient processes in the electrical system of the production well with the downhole reactive power compensator when the power supply is disconnected in order to prevent the risks of false operation of the compensator protection devices. The object: section of a power supply system for a cluster of oil producing wells equipped with electric centrifugal pump installations with downhole reactive power compensators. Methods: positions of theoretical bases of electrical engineering, theory of electric drive, theory of differential equations, numerical methods. Results. The authors developed the mathematical model of the electrical system of the submersible unit for oil production with a downhole reactive power compensator, which enables to investigate transient processes in start-up and shutdown mode of the submersible induction motor. Characteristics of transient processes are obtained in elements of electrical complex of submersible plant for oil production when power supply is switched on and disconnected. It is established that the maximum current surge in the downhole reactive power compensator is 2,56 times with the parameters of the electrical system of the production well accepted in the study. The inventive measures for reducing the number of false actuations of the protection devices are also disclosed