Quasi-stationary Modes Research Articles

STUDY OF THE CURRENT IN THE MULTIELECTRODE PLANT BATH

Active resistance heating multi-electrode ore-thermal furnaces, being in quasi-stationary and transient modes, work in the conditions of electric loop dissymmetry formed by the furnace transformers, current supply and bath caused by the action of different factors of geometric, electromagnetic, thermal and technological character. They worsen the energetic, technological and operational performances. The present methods of studying the electric processes in the furnace loop do not allow in full measure to reveal, consider and eliminate factor actions resulting in phenomena causing electrical duty dissymmetry. Unbalance of the system of currents flowing from the electrode to electrode passing the melt and unbalance of the system of currents flowing directly onto the melt influence the dissymmetry of the furnace loop electrical duty.
 
 The work objective is forming the calculated formulas for determining the resistance heating three-electrode furnace bath “star” and “triangle” currents and by means of them studying the electrode and bath geometrical parameters influence on the mentioned currents.
 
 Materials and methods. The study object is currents flowing in the resistance heating three-phase, three-electrode furnace bath. When carrying out the studies, methods of electrical technology theory and computer mathematic simulation with COMSOL Multiphysics software environment are used.
 
 Results of the study. The study novelty lies in the elaboration of procedure for constructing formulas for calculating the resistance heating three-electrode furnace bath “star” and “triangle” currents with electrode arbitrary location and dissymmetric current system feeding the bath. Influence of the round electrode embedding diameter and the diameter of their dissociation in the three-electrode furnace bath into the currents flowing from the electrode surfaces to the bottom and from the electrode to electrode passing the melt in cases of three-phase symmetric electrode current system and geometrical symmetry of electrode location in the bath is studied.
 
 Findings. Calculation procedure of the resistance heating three-electrode furnace bath “star” and ‘triangle” currents with arbitrary electrode location is developed based on the joint use of the direct admittances and difference-potential coefficients of the equivalent circuits.

Laser fusion cutting: The missing link between gas dynamics and cut edge topography

In laser cutting, the fundamental role of the gas flow for melt removal and kerf formation is generally accepted. Beyond this vague understanding, however, the underlying physical mechanisms are not yet fully understood. In particular, detailed data concerning the momentum and heat transfer between the gas and melt have seldom been reported. This study addresses the local interactions between the cutting gas and kerf surface (melt film surface) in a fundamental way based on a combined experimental, theoretical, and numerical approach. Typical solid-state laser cut edges are analyzed considering the characteristic surface structures and the basic influences of the gas flow on the global and local melt movement. Here, apparent structures in the micrometer range indicate the effect of vortical gas structures close to the wall. Theoretical investigation of the gas boundary layer is conducted by semiempirical equations and the transfer of basic results from the boundary layer theory. It is shown that the boundary layer is in transition between the laminar and turbulent flow, and local flow separations and shock-boundary layer interactions primarily induce spatially periodic and quasistationary instability modes. An improved numerical model of the cutting gas flow confirms the theoretical results and exhibits good agreement with experimental cut edges, reproducing relevant instability modes and quantifying the local momentum and heat transfer distributions between the gas and melt. With the knowledge gained about the underlying physical mechanisms, promising approaches for improvements of the fusion cutting performance are proposed.

Propagation pathways of Indo-Pacific rainfall extremes are modulated by Pacific sea surface temperatures

Intraseasonal variation of rainfall extremes within boreal summer in the Indo-Pacific region is driven by the Boreal Summer Intraseasonal Oscillation (BSISO), a quasi-periodic north-eastward movement of convective precipitation from the Indian Ocean to the Western Pacific. Predicting the spatiotemporal location of the BSISO is essential for subseasonal prediction of rainfall extremes but still remains a major challenge due to insufficient understanding of its propagation pathway. Here, using unsupervised machine learning, we characterize how rainfall extremes travel within the region and reveal three distinct propagation modes: north-eastward, eastward-blocked, and quasi-stationary. We show that Pacific sea surface temperatures modulate BSISO propagation — with El Niño-like (La Niña-like) conditions favoring quasi-stationary (eastward-blocked) modes—by changing the background moist static energy via local overturning circulations. Finally, we demonstrate the potential for early warning of rainfall extremes in the region up to four weeks in advance.

Синхронный многофазный электропривод с управлением по основному энергетическому каналу

One of the options to improve the technical and economic characteristics of a synchronous electric drive is to design it based on an actuating motor with an increased number of phases. However, the characteristics of m-phase (m > 3) synchronous motor associated with the transfer of electromagnetic energy by a whole spectrum of spatial harmonic fields sets the task to develop an automatic control system that considers these features. The method to calculate the characteristics of an m-phase synchronous motor in quasi-stationary modes based on the use of spectral vectors of electromagnetic parameters for its individual substructures as a control object is used. The authors have proposed an approach to study and calculate energy characteristics of m-phase synchronous motor for different control laws implemented on the basis of equations of its design equivalent circuit. The results of the study of the main energy characteristics of the engine for various control laws along the main energy channel are presented. To implement the advantages of a multiphase synchronous motor, it is necessary to force the required mutual arrangement of the flux linkage vectors and stator current for higher spatial harmonics. It can be implemented based on the multi-channel principle of control system design.

METHOD FOR CALCULATION OF DISPERSIONS OF DEPENDENT VARIABLES OF A STOCHASTIC MODEL OF QUASI-STATIONARY OPERATING MODES OF THE MAIN WATER PIPELINE

The subject of research in the article is a stochastic model of quasi-stationary modes of operation of water supply and distribution systems, which adequately describes the actual operating modes of the water supply system for a given time interval and can be used as a basic model for setting and solving problems of optimal stochastic control of the development and operation of supply and distribution systems. water. The goal of the work is to develop a method for calculating estimates of the dispersions of dependent variables depending on the given values of mathematical expectations and dispersions of independent variables for a stochastic model of quasi-stationary modes of operation of the main water conduit as a subsystem of the water supply and distribution system. To achieve this goal, it is necessary to solve the following tasks: to build a deterministic equivalent of a stochastic model of quasi-stationary modes of operation of the main water conduit; calculate estimates of mathematical expectations of dependent variables; calculate estimates of variances of dependent variables. To calculate estimates of the variances of dependent variables depending on the variances of independent variables, we will use the method of statistical linearization. To obtain estimates of mathematical expectations of dependent variables, the deterministic equivalent of the stochastic model of quasi-stationary modes of operation of the main water conduit is solved by the modified Newton method. The following results are obtained: a method for calculating estimates of the dispersions of dependent variables for a stochastic model of quasi-stationary modes of operation of the main water conduit. Conclusions: the paper proposes an approximate method for calculating the statistical properties of dependent variables depending on the statistical properties of the parameters and independent variables of the stochastic model of quasi-stationary modes of operation of the main water conduit. The proposed method is based on the construction of a deterministic equivalent of a stochastic model of quasi-stationary modes of operation of the main water conduit and its use for calculating estimates of variances of dependent variables depending on the given values of mathematical expectations and variances of independent variables. Compared with the simulation method, the proposed approximate method does not require significant time and computational resources. The use of the proposed method was demonstrated by an example.

Modeling of structurization in the adhesive layer in the creation of multilayer objects

In this paper, we propose a thermophysical model of structurization in the adhesive layer during the creation of products by laminating. Modeling is reduced to the solution of a three-layer conjugate thermal conductivity problem. The thermal contact between the layers is assumed to be ideal. It is suggested that structurization activated in the intermediate layer (adhesive layer) can lead to a change in the thermal conductivity coefficient of the adhesive. The lamination process is controlled by a hot roll with a given radius and a fixed temperature. The roll moves along the outer surface at a constant velocity; the force of the roll pressing on the surface determines the size of the contact area and the maximum effective stresses, which are known from the solution of the contact problem and are the parameters in the proposed model. The structurization is represented as a reversible reaction, the forward and reverse rates of which depend on the temperature and the acting stresses. The problem is implemented numerically. The thermal problem is solved using the coordinate splitting difference scheme and the double-sweep method; the kinetic problem is solved using the semi-implicit Euler method. The fields of temperature and structurization level at different moments of time are calculated by varying the values of model parameters. To find stationary or quasi-stationary modes of the structurization process, the behavior of the average integral values of the structurization level and temperature is investigated. It was found that the model parameters have an ambiguous effect on the nature of the temperature distribution and the structurization level; the structurization process does not proceed to its end. The structurization level in the adhesive layer depends on the process parameters (roll temperature, applied pressure and velocity of its movement), as well as on the geometric and physical parameters of the layers.

Quasistationary near-gate plasmons in van der Waals heterostructures

Near-gate plasmons are a new type of plasma oscillations emerging in homogeneous two-dimensional electron systems where a gate provides partial screening of electron-electron interaction. Here we develop a theory of the near-gate plasmons in van der Waals heterostructures comprising a conducting layer separated by a thin insulator from an uncharged disk-shaped gate. We show that in these structures the near-gate plasmons form gate-size-quantized quasi-stationary discrete modes even in the collisionless limit. Belonging to continuum spectrum of two-dimensional plasmons outside of the disk-gate, the near-gate plasmons are manifested as Fano-like resonances in frequency and magnetodispersions of scattering cross-section of the former scattered off the region under the gate. This enables to recover spectrum of the near-gate plasmons in the van der Waals heterostructures using near-field imaging techniques.

СИСТЕМА ОХЛАЖДЕНИЯ ИМПУЛЬСНОГО РЕАКТОРА ПЕРИОДИЧЕСКОГО ДЕЙСТВИЯ

The paper proposes the configuration and composition equipment of the cooling system of the designed periodic pulsed reactor (PPR) of high power. The special features of the PPR are a small flow section, a large heating of the coolant in the power pulse and the impossibility of useful use of thermal energy in the periodic mode of operation. Liquid lithium is proposed as a coolant and heat is discharged through air heat exchangers (AHE). The goal was to achieve compactness and low power consumption, the ability to work with frequent stops and optimize the operation of equipment in pulse modes. For this purpose, high-temperature AHE with a small heat exchange surface and forced air cooling are used, the circulation circuit is divided into two parts - the reactor circuit and the AHE circuit with two circulation pumps and a common drain tank. The separation of the circuit allows to independently perform the operations of starting, stopping and heating the circuits in a periodic mode. The drain tank limits the composition of the equipment exposed to temperature pulses. Numerical studies of the temperature regime of the coolant in the equipment of the PDR cooling system are carried out. The calculations were performed using the TURBOFLOW code in two-dimensional terms for all the main elements of the equipment. Quasi-stationary (nominal and partial power levels) and pulse modes of operation are considered. Calculated characteristics for forced and natural air circulation are obtained. The limits of the air circulation modes under the conditions of non-freezing of the coolant are determined. The obtained values of the maximum temperatures of the coolant: in the pulsed mode is 750 °C, in the quasi-stationary mode - 490 °C with an average power of 15 MW, air flow of 150 m3/s and the size of the AHE in the plan of 5×5 m, 100 panels of 1.08×0.025×5 m.

Quasi-stationary solutions in 1D non-Hermitian systems

Eigenstates exhibit localization at an open edge in a non-Hermitian lattice due to non-Hermitian skin effect. We here explore another interesting feature of non-Hermitian skin effect and predict quasi-stationary solutions, which are approximately time-independent. We show that the transition from such states to eigenstates is dramatically non-perturbative. We consider a non-Hermitian variant of the Su-Schrieffer-Heeger (SSH) model and predict non-topological but robust quasi-stationary zero energy modes.

Coexistence of Coherent Pulses Formed by Superradiant and Quasi-Stationary Modes in a Laser with Low-Q Cavity

Coexistence of Coherent Pulses Formed by Superradiant and Quasi-Stationary Modes in a Laser with Low-Q Cavity

Способ контроля баланса нефти при квазинестационарных режимах работы участка нефтепровода с безнапорным течением

Автоматизированные системы управления используются в нефтепроводном транспорте с целью автоматизации технологических процессов транспортировки нефти и нефтепродуктов, при этом основной задачей является обеспечение надежности и безопасности перекачки, что невозможно без контроля целостности трубопровода. В связи с этим актуальной остается тема обнаружения утечек, требуют продолжения исследования в области повышения надежности автоматизированных систем обнаружения утечек (СОУ). При эксплуатации СОУ особую важность представляет описание процессов заполнения и опорожнения участков трубопровода с безнапорным течением. Скорость установления стационарного режима работы таких участков и участков с полным сечением существенно отличается. Слабые возмущения давления могут приводить к значительному дебалансу расхода нефти и, как следствие, вызывать ложные срабатывания СОУ. Авторами представлен алгоритм вычисления скорости изменения запаса нефти на участке трубопровода при медленном изменении размера самотечной полости, на основании которого предложен способ корректировки уравнения баланса вещества. Показано использование разработанного алгоритма для повышения чувствительности СОУ и уменьшения количества ложных срабатываний. During the operation of leak detection systems (LDS), it is of great importance to describe the processes of filling and emptying pipeline free flow sections. The speed of establishing a stationary operation mode of such sections and full sections is significantly different. Weak pressure perturbations can lead to significant imbalance in the oil flow rate and, as a consequence, cause false LDS positives. The authors present an algorithm for calculating rate of change in oil reserve in the pipeline section with a slow change in the size of gravity cavity, on the basis of which a method for adjusting the substance balance equation is proposed. The use of a developed algorithm is shown to increase the sensitivity of LDS and reduce the number of false alarms.

Coexistence of Coherent Pulses Formed by Superradiant and Quasistationary Modes in a Laser With Low-Q Cavity

Coexistence of Coherent Pulses Formed by Superradiant and Quasistationary Modes in a Laser With Low-Q Cavity

Spectral-Dynamical Peculiarities of Polarization of the Active Medium and Space-Time Empirical Modes of a Laser with a Low-Q Cavity

We have found a set of correlation effects, which are due to the inherent dynamics of the spectral density of polarization of an active medium with strong inhomogeneous broadening of the working transition line and occur if the rate of incoherent relaxation of optical dipole oscillations of the active centers is lower than the rate of optical-field attenuation in the laser cavity. Our analysis is based on the numerical studies of the stationary superradiant laser generation during continuous pumping with self-locking of some of the quasistationary modes. For the purposes of studying the detected effects, the methods of comparative analysis of the dynamic spectra of polarization and the field have been developed. In these methods, the time-frequency and space-time empirical modes of the spectra are used, which are determined by orthogonal eigenfunctions of special correlation matrices. The interconnection of the superradiance phenomena and mode self-locking in the considered class of lasers with low-Q cavities is discussed.

Stability of the interface between two thin liquid layers under tangential high frequency vibrations

In this paper, a system of two equally thin layers of immiscible incompressible isothermal ideal liquids under high frequency horizontal harmonic vibrations is considered theoretically. The vessel containing the liquids is assumed to be closed, of rectangular form with weakly-deformable side borders and infinitely long in horizontal direction. Previous studies showed that, for significantly thin layers, the main instability in the system, oscillatory Kelvin-Helmholtz instability, should be the long-wave instability. Therefore, the problem was solved analytically using “shallow water” approximation. For all equations, a formal expansion with respect to two small parameters was used: one associated with a small ratio of the vertical to horizontal scale and another with small perturbations of the flat interface. Evolutionary equations were derived for the interface in the main order of expansion for vibration intensity less than a threshold value for oscillatory Kelvin-Helmholtz instability (subcritical area). The solutions found for these evolutionary equations correspond to traveling waves with soliton or cnoidal interfacial surface. The soliton profile is a limiting case of the cnoidal profile. The maximum speed of these waves was determined. It was demonstrated that the obtained solutions exist only in the subcritical area of parameters and from the critical level subcritical bifurcation emerges. For special case of traveling waves in a quasi-stationary mode (i.e. with static interface) also referred to as a “frozen wave”, a numerical analysis of linear stability was performed using a Fourier series expansion in a horizontal coordinate. The instability of quasi-stationary modes to small disturbances was demonstrated.

Floquet engineering of localized propagation of light in a waveguide array

The light propagating in a waveguide array or photonic lattice has become an ideal platform to control light and to mimic quantum behaviors in a classical system. We here investigate the propagation of light in a coupled waveguide array with one of the waveguides periodically modulated in its geometric structure or refractive index. Within the framework of Floquet theory, it is interesting to find that the light shows the localized propagation in the modulated waveguide as long as bound quasistationary modes are formed in the band-gap area of the Floquet eigenvalue spectrum. This mechanism gives a useful instruction to confine light via engineering the periodic structure to form the bound modes. It also serves as a classical simulation of decoherence control via temporally periodic driving in open quantum systems.

Statistical analysis of m/n = 2/1 locked and quasi-stationary modes with rotating precursors at DIII-D

A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers m = 2 and n = 1 at DIII-D. The analysis of 22500 discharges shows that more than 18% of disruptions are due to locked or quasi-stationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance li divided by the safety factor at 95% of the poloidal flux, q95, is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as dedge, performs comparably to in its ability to discriminate disruptive locked modes. Out of all parameters considered, dedge also correlates best with the duration of the locked mode. Disruptivity following a m/n = 2/1 locked mode as a function of the normalized beta, , is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between and q95 in the DIII-D operational space. Within 50 ms of a locked mode disruption, average behavior includes exponential growth of the n = 1 perturbed field, which might be due to the 2/1 locked mode. Surprisingly, even assuming the aforementioned 2/1 growth, disruptivity following a locked mode shows little dependence on island width up to 20 ms before the disruption. Separately, greater deceleration of the rotating precursor is observed when the wall torque is large. At locking, modes are often observed to align at a particular phase, which is likely related to a residual error field. Timescales associated with the mode evolution are also studied and dictate the response times necessary for disruption avoidance and mitigation. Observations of the evolution of during a locked mode, the effects of poloidal beta on the saturated width, and the reduction in Shafranov shift during locking are also presented.

The use of a topological list for calculating the parameters of electric-power systems on the basis of the node-voltage method

The software implementation of the node-voltage equations for calculating the parameters of electric-power systems on the basis of the topological list is considered. Of the well-known modifications of the node-voltage method, it is proposed to use the equations for node voltages in the form of a current balance when specifying a constant-conductivity load. To eliminate the harmonic components during calculations, the equation for each element of the electric-power system is represented in the Park–Gorev axes. When forming the matrices of the nodal conductivities and specifying currents, a topological list that is based on the principle of piecemeal contributions is used. The key advantages of the method that is based on the topological list are that it is unnecessary to observe the order of numbering rows and that this method is highly algorithmic, thus providing the minimization of the computational efforts in compiling equations on a computer. The essence of the piecemeal-contribution principle lies in the successive formation of matrix coefficients, as row-by-row processing of the topological list is performed. An algorithm for the formation of equations according to the node-voltage method using the topological list in the form of a block diagram is presented. Calculation using the node-voltage method on the basis of the topological list is an independent task, as well as representing a component of more complex types of calculations, such as optimization of the normal modes, stability analysis, reliability assessment, etc. The interrelations between individual components of the process of solving the problem of calculating stationary and quasi-stationary operating modes of the electric-power system with respect to input and output information are shown. The formation of the equations of the structural elements in stationary and quasi-stationary modes of the electric-power system of a factory is based on the linearization of the initial node-voltage equations.

Quantization of electromagnetic field and analysis of Purcell effect based on formalism of scattering matrix

We have developed a rigorous self-consistent approach for the quantization of electromagnetic field in inhomogeneous structures. The approach is based on utilization of the scattering matrix of the system. Instead of the use of standard periodic Born-Karman boundary conditions, we use the quantization condition implying equating eigenvalues of the scattering matrix (S-matrix) of the system to unity (S-quantization). In the trivial case of uniform medium boundary condition for S-quantization is nothing but periodic boundary condition. S-quantization allows calculating modification of the spontaneous emission rate for arbitrary inhomogeneous structure and direction of the emitted radiation. S-quantization solves the long-standing problem coupled to normalization of the quasi-stationary electromagnetic modes. Examples of application of S-quantization for the calculation of spontaneous emission rate for the cases of Bragg reflector and microcavity are demonstrated.

Radiative plasmon polaritons in multilayer structures with a two-dimensional electron gas

Two-dimensional plasmon polaritons are analyzed for a typical experimental configuration in which a layer of two-dimensional electrons with a finite mobility lies on the top of a dielectric waveguide formed by the substrate (a wafer of finite thickness). Two-dimensional plasmons couple strongly to the radiative modes of this dielectric waveguide. It is shown that, as a result of the competition between collisional and radiative processes, a family of eight quasi-stationary normal modes arises. Six of them decay carrying energy to infinity. The two remaining plasmon-polariton modes are nonradiative. One of these modes, the TM-type plasmon polariton, in the limiting case where retardation is disregarded corresponds to the conventional longitudinal two-dimensional plasmon. The other mode, the TE-type plasmon polariton, exists only for a finite thickness of the substrate. All of them are characterized by different dispersion relations of the complex frequency ω(q) = Reω + iImω and differ in both polarization (longitudinal and transverse) and symmetry with respect to the direction of decay (symmetric and asymmetric). The latter modes decay slowly, propagating into free space to plus or minus infinity. The conditions under which the Q factors of certain modes are arbitrarily high are found. In this case, Imω(q0) = 0, and dissipative losses in the two-dimensional electron gas are compensated by external sources. As a result, the reflection coefficient for a plane wave whose angle of incidence is determined by the vector q0 vanishes.

Stochastic model and method of zoning water networks

Water consumption at different time of the day is uneven. The model of steady flow distribution in water-supply networks is calculated for maximum consumption and effectively used in the network design and reconstruction. Quasi-stationary modes, in which the parameters are random variables and vary relative to their mean values are more suitable for operational management and planning of rational network operation modes.Leaks, which sometimes exceed 50 % of the volume of water supplied, are one of the problems in water-supply systems. One of the ways to reduce leaks is zoning (overpressure zone definition) and pressure regulators installation.The method of reengineering water networks by their zoning and pressure regulators installation was developed in the paper. Its implementation provides a significant reduction of the total overpressure in the water network nodes, water leak volumes and saving material and energy resources.The improved method for zoning the water network is based on the stochastic model of quasi-stationary modes in the water supply and distribution systems, and pressure regulators parameters optimization for each determined zone.