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This paper presents the results of a study on impact of high-power heat load and tungsten (W) surface carbidization on its structural-phase composition and physical-mechanical properties. In this r...

In this research, samples of an alloy with a bimodal structure were studied on the basis of a previously developed technology for obtaining hydrogen storage materials based on the Ti-Al-Nb system. The results of SPS of mechanically activated powder mixtures of the Ti-Al-Nb system at a temperature of 1300 °C make it possible to obtain an alloy with a predominantly bimodal structure. However, an insignificant presence of TiAl3, AlNb2 phases, and unreacted niobium is still observed in the structure. The mechanical properties of alloys of the Ti-Al-Nb system after sintering show abnormally low values of strength and ductility (less than 150 MPa). Two-stage heat treatment of alloys of the Ti-Al-Nb system leads to the decomposition of large precipitates of TiAl3 with the formation of O-phase nuclei, as well as to the complete dissolution of unreacted niobium and AlNb2 phases. Heat treatment of alloys of the Ti-Al-Nb system contributes to an increase in its strength by approximately 10 times (1310 MPa, MA-180), and ductility by 2 times (1322 MPa, MA-20). The surface fracture of samples obtained after testing is characterized by intergranular (intercrystalline) brittle fracture with “river” or “step” features.

The purpose of the study is to analyze the regulatory and legal support for the adaptation of service members to civilian life in the United States, France, and Germany to identify elements that could be useful for implementation in Ukrainian legislation. The 5 stages of adaptation that each service member goes through after completing his/her service when returning to civilian life are identified and analyzed. It is found that all analyzed countries begin the adaptation process several months (or years) before the end of service. In addition, former service members consistently receive financial assistance. The obtained results can be used by scientists for further analysis of regulatory and legal support and, on its basis, direct implementation of procedures for adaptation of service members to civilian life.

Purpose The purpose of this paper is to determine how the shape of the container affects the efficiency of a traveling magnetic field (TMF) stirring. Design/methodology/approach The modeling approach is based on finite element software Comsol which includes harmonic electromagnetic (EM), transient CFD and particle tracing modules. For evaluating efficiency of stirring the particle, homogenization parameter is used. Findings It has been determined that the use of an elliptical cylinder-shaped vessel allows better heat removal from the side surface and, at the same time, the stirring efficiency does not drop significantly. Practical implications The results of the work can be used in the design of EM stirring installations in which exothermic reactions occur. Originality/value The transient simulation of particle transport in a TMF-driven melt flow gives the opportunity to estimate the efficiency of stirring process in different vessel shapes.

Purpose The purpose of this paper is to search optimal shape of soft magnetic composite-based inserts used to compensate the working gap between the liquid metal and the induction stirrer in metallurgical installations. Design/methodology/approach The study was based on numerical simulation of electromagnetic processes in frequency domain. To optimize inserts shape, the Nelder–Mead method was used. The maximum of integral electrodynamic force along x-axis was chosen as the objective function. All simulations were performed in finite element software package Comsol Multiphysics. Findings Optimal inserts shape was determined, at which the value of integral electrodynamic force along x-axis increased by 20% from 692 to 792 N. Originality/value Magnetic concentrators based on soft magnetic composite materials have long been used in high-frequency systems; at the same time, their use in low-frequency systems has not been previously considered in detail. The study of the shape effect of concentrators on the effectiveness of electromagnetic field in a liquid metal in a three-dimensional formulation was carried out for the first time.

We derive. the ensemble- and time-averaged mean-squared displacements (MSD, TAMSD) for Poisson-reset geometric Brownian motion (GBM), in agreement with simulations. We find MSD and TAMSD saturation for frequent resetting, quantify the spread of TAMSDs via the ergodicity-breaking parameter and compute distributions of prices. General MSD-TAMSD nonequivalence proves reset GBM nonergodic.

We explore model performance for the Alfvén Wave Solar atmosphere Model (AWSoM) with near-9 real-time (NRT) synoptic maps of the photospheric vector magnetic field. These maps, produced by 10 assimilating data from the Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamics Obser-11 vatory (SDO), use a different method developed at the National Solar Observatory (NSO) to provide 12 a near contemporaneous source of data to drive numerical models. Here, we apply these NSO-HMI-13 NRT maps to simulate three Carrington rotations (CRs): 2107-2108 (centered on 2011/03/07 20:12 14 CME event), 2123 (integer CR) and 2218-2219 (centered on 2019/07/2 solar eclipse), which together 15 cover a wide range of activity level for solar cycle 24. We show simulation results, which reproduce 16 both extreme ultraviolet emission (EUV) from the low corona while simultaneously matching in situ 17 observations at 1 au as well as quantify the total unsigned open magnetic flux from these maps. 18

To simulate solar Coronal Mass Ejections (CMEs), predict their time of arrival and geomagnetic impact, it is important to accurately model the background solar wind conditions in which CMEs propaga...

Cancer genetics has uncovered many tumor-suppressor and oncogenic pathways, but few alterations have revealed mechanisms involved in tumor spreading. Here, we examined the role of the third most significant chromosomal deletion in human melanoma that inactivates the adherens junction gene NECTIN1 in 55% of cases. We found that NECTIN1 loss stimulates melanoma cell migration in vitro and spreading in vivo in both zebrafish and human tumors specifically in response to decreased IGF1 signaling. In human melanoma biopsy specimens, adherens junctions were seen exclusively in areas with low IGF1 levels, but not in NECTIN1-deficient tumors. Our study establishes NECTIN1 as a major determinant of melanoma dissemination and uncovers a genetic control of the response to microenvironmental signals.

The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via an unobservable controllable MJP (Markov jump process) with finite-state space. Observations are formed by low-frequency counting processes of packet losses and timeouts and a high-frequency compound Poisson process of packet acknowledgments. The information transmission through the TCP-equipped channel is considered a stochastic control problem with incomplete information. The main idea to solve it is to impose the separation principle on the problem. The paper proposes a mathematical framework and algorithmic support to implement the solution. It includes a solution to the stochastic control problem with complete information, a diffusion approximation of the high-frequency observations, a solution to the MJP state filtering problem given the observations with multiplicative noises, and a numerical scheme of the filtering algorithm. The paper also contains the results of a comparative study of the proposed state-based congestion control algorithm with the contemporary TCP versions: Illinois, CUBIC, Compound, and BBR (Bottleneck Bandwidth and RTT).

A model is developed for an electromagnetic stirrer using a traveling magnetic field. Electromagnetic and hydrodynamic problems are simultaneously solved for a two-dimensional case by a finite element method. The behavior of impurities in a turbulent flow is calculated using the Stokes law. A nonstationary magnetic field is shown to be applied. The calculated spatial distribution of impurities has a homogeneous character in the liquid metal volume. The model is verified by measuring the magnetic induction in an experimental setup.

This paper presents the research results of hydrogen plasma effect on the surface structure of the TGP-56 beryllium. In the linear simulator, the operating conditions of the first wall of ITER are simulated. Beryllium was irradiated with hydrogen plasma at surface temperatures of ~360 °C, ~800 °C, and ~1200 °C, depending on its location in the ITER chamber; with a different number of pulses with a duration of each pulse of 500 s. Samples of irradiated beryllium were subjected to a set of material studies. Experimental data were obtained on the change in the structure of the surface and edges of the beryllium samples after the plasma effect. It was found that at normal (2 MW/m2) and increased (4.7 MW/m2) heat fluxes on the first wall of the ITER, the edges and beryllium surface have good resistance to erosion. Under critical conditions close to the melting point, beryllium strongly erodes and evaporates. It has been established that this material has a high resource resistance to hydrogen plasma effect in the ITER under operating conditions.

We perform a series of time dependent Magnetohydrodynamic simulations of the HD 189733 star-planet system in order to predict radio transit modulations due to the interaction between the stellar wind and planetary magnetic field. The simulation combines a model for the stellar corona and wind with an exoplanet that is orbiting the star in a fully dynamic, time-dependent manner. Our simulations generate synthetic radio images that enable us to obtain synthetic radio lightcurves in different frequencies. We find a clear evidence for the planetary motion in the radio light curves. Moreover, we find specific repeated features in the light curves that are attributed to the passage of the planetary magnetosphere in front of the star during transit. More importantly, we find a clear dependence in the magnitude and phase of these lightcurve features on the strength of the planetary magnetic field. Our work demonstrates that if radio transits could be observed, they could indeed provide information about the magnetic field strength of the transiting exoplanet. Future work to parameterize these lightcurve features and their dependence on the planetary field strength would provide tools to search for these features in radio observations datasets. As we only consider the thermal radio emission from the host star for our study, very sensitive radio interferometers are necessary to detect these kinds of planetary transit in radio., 19 Pages, 10 Figures

Despite a long history and a clear overall understanding of properties of random walks on an incipient infinite cluster in percolation, some important information on it seems to be missing in the literature. In the present work, we revisit the problem by performing massive numerical simulations for (sub)diffusion of particles on such clusters. Thus, we discuss the shape of the probability density function (PDF) of particles' displacements, and the way it converges to its long-time limiting scaling form. Moreover, we discuss the properties of the mean squared displacement (MSD) of a particle diffusing on the infinite cluster at criticality. This one is known not to be self-averaging. We show that the fluctuations of the MSD in different realizations of the cluster are universal, and discuss the properties of the distribution of these fluctuations. These strong fluctuations coexist with the ergodicity of subdiffusive behavior in the time domain. The dependence of the relative strength of fluctuations in time-averaged MSD on the total trajectory length (total simulation time) is characteristic for diffusion in a percolation system and can be used as an additional test to distinguish this process with disorder-induced memory from processes with otherwise similar behavior, like fractional Brownian motion with the same value of the Hurst exponent., Comment: 15 pages, 5 figures

The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules obtainable from a set of atomic species grow exponentially with the size of the system, limiting the efficiency of classical sampling algorithms. On the other hand, quantum computers can provide an efficient solution to the sampling of the chemical compound space for the optimization of a given molecular property. In this work, we propose a quantum algorithm for addressing the material design problem with a favourable scaling. The core of this approach is the representation of the space of candidate structures as a linear superposition of all possible atomic compositions. The corresponding ‘alchemical’ Hamiltonian drives the optimization in both the atomic and electronic spaces leading to the selection of the best fitting molecule, which optimizes a given property of the system, e.g., the interaction with an external potential as in drug design. The quantum advantage resides in the efficient calculation of the electronic structure properties together with the sampling of the exponentially large chemical compound space. We demonstrate both in simulations and with IBM Quantum hardware the efficiency of our scheme and highlight the results in a few test cases. This preliminary study can serve as a basis for the development of further material design quantum algorithms for near-term quantum computers., Chemical Science, 12 (12), ISSN:2041-6520, ISSN:2041-6539

The paper is devoted to the optimal state filtering of the finite-state Markov jump processes, given indirect continuous-time observations corrupted by Wiener noise. The crucial feature is that the observation noise intensity is a function of the estimated state, which breaks forthright filtering approaches based on the passage to the innovation process and Girsanov&rsquo, s measure change. We propose an equivalent observation transform, which allows usage of the classical nonlinear filtering framework. We obtain the optimal estimate as a solution to the discrete&ndash, continuous stochastic differential system with both continuous and counting processes on the right-hand side. For effective computer realization, we present a new class of numerical algorithms based on the exact solution to the optimal filtering given the time-discretized observation. The proposed estimate approximations are stable, i.e., have non-negative components and satisfy the normalization condition. We prove the assertions characterizing the approximation accuracy depending on the observation system parameters, time discretization step, the maximal number of allowed state transitions, and the applied scheme of numerical integration.

Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties of molecular and condensed matter systems. However, the quality of this procedure relies on the availability of rigorous electronic structure calculations. The development of quantum processors has shown great potential for the efficient evaluation of accurate ground and excited state energies of molecular systems, opening up new avenues for molecular dynamics simulations. In this work, we address the use of variational quantum algorithms for the calculation of accurate atomic forces to be used in AIMD. In particular, we provide solutions for the alleviation of the statistical noise associated with the measurements of the expectation values of energies and forces, as well as schemes for the mitigation of the hardware noise sources (in particular, gate infidelities, qubit decoherence, and readout errors). Despite the relative large error in the calculation of the potential energy, our results show that the proposed algorithms can provide accurate MD trajectories in the microcanonical (constant energy) ensemble. Furthermore, exploiting the intrinsic noise associated to the quantum measurement process, we also propose a Langevin dynamics algorithm for the simulation of canonical, i.e., constant temperature, dynamics. Both algorithms (microcanonical and canonical) are applied to the simulation of simple molecular systems such as H2 and H3+. Finally, we also provide results for the dynamics of H2 obtained with IBM quantum computer ibmq_athens.

Stock Company “NIIEFA,” Russia, within the framework of the international project ITER produces and supplies the PF1 poloidal field coil. The choice of design solutions, materials, and technologies is under high electromagnetic and thermal loads. The PF1 coil uses liquid helium as a cooling system, which is fed into joints through helium inlets. Joints are bimetallic structural components obtained by explosion welding technologies and tungsten inert gas (TIG)-welding with a complex structural profile. Materials used: austenitic stainless steel, bimetallic copper-steel; bonded technology: TIG-welding, explosion welding. The quality of materials, explosion border and welds are subject to the highest requirements of European standards. Technologies of industrial manufacture of the PF1 coil require the use of nondestructive testing (NDT) procedures, caused by complex weld profile, small testing zone, and heterogeneity of welds. This paper shows the technology and NDT equipment for testing material and welds of the PF1 coil.

The paper describes the method, mathematical model and results of electromagnetic stirring processes investigation. A complex mathematical model of an electromagnetic stirrer, considering electromagnetic and hydrodynamic processes, has been developed. Using the developed model, the problem of melt flow control in a finite element formulation was solved using the CAE software package, which provided a tool for studying electromagnetic mixing processes. The processes under the influence of an electromagnetic stirrer built into a continuous casting machine of large-format slabs using computer simulation were investigated, which allowed determining typical operating modes: the optimal frequency is 1 Hz, the current strength is at least 550 A, and the design parameters of inductors.

Shape optimization occupies an important place in the development of MHD-stirrer for liquid metal, allowing to reduce economic and time costs. For all importance and relevance, there is still no unequivocal opinion as to which optimality criterion should be chosen: integral electromechanical force, integral melt velocity or time of technological process, for example, equalizing temperature in the melt volume. Present paper is devoted to comparing results of magnetic core optimization for MHD-stirrer with a traveling EM field for listed optimality criteria. As a parameter, by which efficiency of obtained result was evaluated, the time taken to equalize temperature in the melt volume was chosen.

Volume heating used during silicon purifying permit uniformly temperature distribution at all bowl. Forced stirring with quartz devices is associated with high process failure and low efficiency. To intensify the process, it is proposed to use electromagnetic stirring by a traveling magnetic field. Optimal shape design of stirrer can be obtained by a multiobjective optimization method based on gradient descent to reduce primary weight and stirring time, simultaneously. Objective function is defined from magnetohydrodynamic problem considered in this article. Also, different version of magnetic core is examined. This coupled-field problem is decoupled to separated magnetic, hydrodynamic and thermal problems and analyzed by means of finite element method, while the optimal design problem is solved by gradient-based algorithm and best solution is chosen.

In this paper, we investigate the transient response of Lorentz force at finite magnetic Reynolds numbers $ {R_{m}}$ on an electrically conducting rectangular bar that is strongly accelerated in the presence of a localized magnetic field. This is done through numerical simulations utilizing a coupled finite-difference boundary element approach. The results show good qualitative agreement with existing experiments with a circular cylinder. The Lorentz force rise time is seen to be a linear function of $ {R_{m}}$ . The linear dependence of Lorentz force on $ {R_{m}}$ is found to be valid only for low values of $ {R_{m}}$ , after which the slope decays leading to an apparent saturation in the Lorentz force at sufficiently large values of $ {R_{m}}$ . Our results provide important information for the development of Lorentz force flow meters for transient flow applications.

Doping of pristine materials can change their chemical and electrical properties. Namely nitrogen doping of graphene results in modulation of electronic properties of graphene. In this work we present experimental results on nitrogen doped graphene fabricated in two steps. At first, the graphene samples were synthesized by a chemical vapor deposition method on copper foils. Then they were treated with ammonia radio frequency discharge plasma. The prepared samples were investigated by atomic-force microscopy (AFM), scanning electron microscopy (SEM), Raman spectroscopy, optical absorption spectroscopy including Fourier transform infrared spectroscopy (FTIR), X-ray and ultraviolet photoelectron spectroscopy. In doped graphene a dependence of N-atom concentration on the treatment parameters has been revealed. A maximum doping level of 3 atomic % has been obtained and the shift of valence band maximum of 0.2 eV was observed at this concentration of nitrogen.

The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.

Ringing mode of atomic force microscopy (AFM) enables imaging the surfaces of biological samples, cells, tissue, biopolymers, etc. to obtain unique information, such as the size of molecules pulled by the AFM probe from the sample surface, heights of the sample at different load forces, etc. (up to eight different imaging channels can be recorded simultaneously, which is in addition to five channels already available in other rival modes). The imaging can be done in both air (gases) and liquid (buffers). In addition, the images obtained in ringing mode do not have several common artifacts and can be collected up to 20× faster compared to the rival imaging modes. Here we describe a step-by-step approach to collect images in ringing mode applied to biological and soft materials in general. Technical details, potential difficulties, and points of special attention are described.

Atomic force microscopy (AFM) indentation analysis of cells is a unique method of measuring stiffness of the cell body and physical properties of its pericellular coat. These cell parameters correlate with cells of abnormality and diseases. Viable biological cells can be studied with this method directly in a culture dish with no special preparation. Here we describe a step-by-step method to analyze the AFM force-indentation curves to derive cell mechanics (the modulus of elasticity of the cell body) and the parameters of the pericellular coat (density and the thickness of the coat layer). Technical details, potential difficulties, and points of special attention are described.

Solar Energetic Particles (SEPs) are an important aspect of space weather. SEP events posses a high destructive potential, since they may cause disruptions of communication systems on Earth and be fatal to crew members onboard spacecrafts and, in extreme cases, harmful to people onboard high altitude flights. However, currently the research community lacks efficient tools to predict such hazardous threat and its potential impacts. Such a tool is a first step for mankind to improve its preparedness for SEP events and ultimately to be able to mitigate their effects. The main goal of the presented research effort is to develop a computational tool that will have the forecasting capability and can be serve in operational system that will provide live information on the current potential threats posed by SEP based on the observations of the Sun. In the present paper the fundamentals of magneto-hydrodynamical (MHD) simulations are discussed to be employed as a critical part of the desired forecasting system.

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole picture, which offers a better starting point for the expansion of the system wave function. The state of the molecular system at study is parametrized so as to constrain the sampling of the corresponding wave function within the sector of the molecular Fock space that contains the desired solution. To this end, we explore different mapping schemes to encode the molecular ground state wave function in a quantum register. Taking advantage of known post-Hartree-Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the unitary coupled-cluster (UCC) method within the variational quantum eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC, with important advantages compared to the straightforward translation of the classical coupled-cluster counterpart. In particular, we show how a single Trotter step in the expansion of the system wave function can accurately and efficiently reproduce the ground-state energy of simple molecular systems.

Fractal analysis of the cell surface is a rather sensitive method which has been recently introduced to characterize cell progression toward cancer. The surface of fixed and freeze-dried cells is imaged with atomic force microscopy (AFM) modality in ambient conditions. Here we describe the method to perform the fractal analysis specifically developed for the AFM images. Technical details, potential difficulties, points of special attention are described.

In modern times, exposure to a liquid metal by a travelling magnetic field is widely applied. There are laboratory studies on the processes of stirring and crystallization under the action of a traveling magnetic field. However, in the majority of studies it is assumed that the inductor power supply of the linear induction machine is carried out by a symmetrical three-phase system of currents with an equal phase shift, which, in some cases, is not quite correct. To approximate the model to real operating conditions, a numerical simulation of the magnetic field and the flow of liquid metal was carried out when supplied from a power source of symmetric three-phase voltage. The distortion of magnetic field, which, in turn, causes an nonuniform distribution of forces and the flow of a liquid metal, is shown. Evaluation of asymmetrical effect on the liquid metal flow was carried out by means of finite element method. That effect is caused by different coefficients of mutual coils induction of the linear induction machine, which is confirmed by experimental data. © Published under licence by IOP Publishing Ltd. Russian Foundation for Basic Research, RFBR: 17-48-590539 r a Ural Federal University, UrFU The work of Institute of Continuous Media Mechanics team is supporting by the RFBR grant 17-48-590539 r a and the work of Ural Federal University team is supporting by Act 211 Government of the Russian Federation, contract 02.A03.21.0006.

In the present work the influence of low frequency modulation of a travelling magnetic field (TMF) on a process of generation of electro-vortex flows in electrically conducting media are numerically and experimentally investigated. The measurements are carried out on a low melting temperature GaZnSn alloy by means of Ultrasonic Doppler Velocimetry. For numerical simulation, Comsol Multiphysics software was used. The dependencies of average and pulsating Reynolds numbers on the magnitude of electromagnetic impact and two modes of low frequency modulation are considered. A positive influence of reversed TMF modulations on the stirring process is determined. In particular the formation of a small-scale vortex structure in the main volume of liquid media. © Published under licence by IOP Publishing Ltd. Russian Foundation for Basic Research, RFBR: 17-48-590539_r_a Ural Federal University, UrFU The work of Institute of Continuous Media Mechanics team is supported by the RFBR grant 17-48-590539_r_a and the work of Ural Federal University team is supported by Act 211 Government of the Russian Federation, contract є 02.A03.21.0006.

This paper describes some aspects of the mathematical modeling and the experimental study of the magnet-free synchronous reluctance motor (SynRM) of IE5 efficiency class (rated power is 750 W, rated speed is 3000 rpm, rated efficiency is 89.5%). The proposed mathematical model allows minimizing the number of the boundary problems which is to be solved and allows calculating power, losses, torque waveform etc. Also the results of experimental comparison of the IE5 magnet-free SynRM prototype and the serially produced magnet-free SynRM of IE4 efficiency class (rated power is 750 W, rated speed is 3000 rpm, rated efficiency is 85.6%) are presented.

The article is devoted to the comparative research of performances of controlled drives with a synchronous reluctance motor (SynRM) and with an induction motor (IM) in a pump application. In this study the performances of the motors are represented as iso efficiency maps. The issues include the calculation of the payback time of commuting of the IM drive to the SynRM drive. It is shown that the application of SynRM in a pump drive is able to assist to significant improving of efficiency of pump installation.

This paper presents the results of the development and pilot study of the highly efficient synchronous reluctance motor. The results include a detailed comparative analysis of the performance values of various modes of the developed synchronous reluctance motor and the series induction motor of the same power made in the same housing. These motors heating and other parameters have been compared. The prospects for application of the developed synchronous reluctance motor in a variable frequency drive (for example, in a fan/pump drive) are estimated.

While he derived the equation for the radiation force, Dirac (1938) mentioned a possibility to use different choices for the 4-momentum of an emitting electron. Particularly, the 4-momentum could be non-colinear to the electron 4-velocity. This ambiguity in the electron 4-momentum allows us to assume that the mass of emitting electron may be an operator, or, at least, a 4-tensor instead of being the usually assumed scalar, which relates the 4-velocity of a bare charge to the total momentum of a dressed point electron, the latter being a total of the momentum of the bare electron and that of the own electromagnetic field. On applying the re-normalization procedure to the mass operator, we arrive at an interesting dichotomy. The first choice (more close to traditional one) ensures the radiation force to be orthogonal to the 4-velocity. In this way the re-normalization results in the Lorentz-Abraham-Dirac equation or in the Eliezer equation. However, the 4-momentum of electron in this case is not well defined: the equality in the relativistic entity (E/c)^2=m^2c^2+p^2 appears to be broken and even the energy is not definite positive. The latter is an underlying reason for the 'run-away' solution. The other choice is to require the radiation force to be orthogonal to the 4-momentum (not to the 4-velocity). In this case the energy and momentum are well-defined and obey the relationship (E/c)^2=m^2c^2+p^2. Remarkably, the equations of a particle's motion in this case differ significantly from all the known versions. They appear to be well founded. They are simple, easy to solve, and can be applied to simulate the particle motion in the focus of an ultra-bright laser.