Baskakov A.V., Volkov N.P.
The controllability of transient processes in some problems of reactor dynamics is considered. In this case, the mathematical model of reactor dynamics is described by a system of integrodifferential equations consisting of a time-dependent anisotropic multivelocity kinetic transport equation and the balance equation of delayed neutrons. We have formulated the linear problem of controlling transient processes in nuclear reactors by means of a distributed control action on internal sources of neutrons, as well as nonlinear problems of control by means of distributed control actions on the absorption coefficient and scattering indicatrix. The sought control actions depend on the spatial and velocity coordinates. The existence and uniqueness theorems for these control actions have been proven by reducing the studied control problems to equivalent systems of integral equations. The existence and uniqueness of the solution of this system of integral equations has been proven by the method of successive approximations, which makes it possible to construct an iterative scheme for the numerical calculation of the mathematical model of transient processes in a given reactor. Sufficient conditions for the controllability of these processes have been obtained. In conclusion, a connection is given between the problems of control and the problems of observation, which make it possible to reconstruct either the function of internal sources or the absorption coefficient or the scattering indicatrix from the given information. Keywords: control of transient processes, reactor dynamics, sufficient conditions of controllability
Katunin Yu.V., Stenin V.Ya.
The TCAD simulation of the 65-nm bulk CMOS matching logic element based on a STG DICE cell with the Exclusive OR combinational logic has been presented. This element is designed for the content addressable memory (associative memory) and the translation lookaside buffers for the 65-nm CMOS bulk technology. The combinational logic consists of two tristate inverters. The STG DICE (Spaced Transistor Groups DICE) is different from the standard DICE (Double Interlocked Cell) in that the transistors are separated into two groups. That is why charge collection from the track of single nuclear particles impacting on one of two groups does not lead to the upset state of this memory cell. Noise immunity of the matching element based on the STG DICE cell increases by the separation of its transistors into two blocks. Each block consists of one group of transistors of the STG DICE cell and transistors of one of two tristate inverters. Charge collection with tracks of nuclear particles has been simulated using tracks along the normal to the chip surface. Linear energy transfers on tracks were in the range of 10–60 MeV cm2/mg. Taking into account the silicon doping under the 400-nm-thick separating oxide layer, the main part of charges was collected from the layer of the silicon at depths of 400–850 nm from the surface of the chip. Data upsets in STG DICE cells with tracks along the normal to the chip surface were absent at charge collection from tracks onto the linear energy transfer up to 60 MeV cm2/mg. In the combinational Exclusive NOR logic, noise pulses up to 0.6 ns in the range of the energy transfer of 30–60 MeV cm2/mg can occur. Keywords: logic element, simulation, single nuclear particle, failure tolerance, tracks of nuclear particles, memory cell
Ermolaeva N.V., Ratushnyi V.I., Sevastyanov D.A.
A device for detection and monitoring of gases (methane, propane, carbon monoxide, and hydrogen) in air and for measurements of physical quantities (temperature, humidity) compatible with any Android smartphone has been described. The smartphone is used to display information and to control display modes on the screen. The measurement is performed by the microcontroller; therefore, the measuring device function is determined by a set of sensors connected to the microcontroller and is independent of a smartphone model. The proposed device can support simultaneous operation of up to five sensors, but each sensor can be replaced by the principle of modularity. Communication of the microcontroller and a smartphone occurs through Bluetooth wireless technology. This makes it possible to remotely determine the concentration of hazardous and flammable gases in basements of buildings and constructions, engineering communications, and boiler houses. The device is powered by batteries. A power bank laptop charger is used to recharge the batteries. The device allows locally controlling the concentration of four gases simultaneously, as well as the temperature and humidity, and has a low weight. The functionality of the smartphone allows using the proposed device to replicate the operational information to interested subscribers. Domestic and industrial use of this device is shown. Keywords: portable gas analyzer, smartphone, microcontroller, temperature and humidity sensor, detection and monitoring of gases, methane, propane, carbon monoxide, hydrogen
Safonova D.V., Demina M.V., Kudryashov N.A.
The problem of constructing and classifying stationary equilibria of point vortices on a cylinder is studied. The motion of a multivortex system in a background flow is described by the Helmholtz equation with an additional term. A polynomial method is used to describe point vortices. The main idea of this method is that the roots of polynomials correspond to the positions of point vortices. A differential equation for finding stationary configurations for a multivortex system on the cylinder in zero background flow is obtained. The case of a point vortex system consisting of point vortices with constant circulations Γ1 and Γ2 = –μΓ1) is considered in detail. An ordinary differential equation for this system and its polynomial solutions are obtained. Configurations with the number of vortices less than six are considered with the use of two polynomials without multiple and common roots that possess total degree less than six. New vortex configurations and four configurations with a free parameter are found. Most of the stationary vortex configurations are found for the first time. Keywords: point vortices, stationary configuration, vortices on a cylinder
Mathematical models of propagation of pulses through axons from one neuron to others have been considered with the focus on the FitzHugh–Nagumo model. The analytical properties of this model have been studied. It has been shown that the system of equations for the description of the FitzHugh–Nagumo model does not pass the Painleve test and, therefore, does not have a general solution. The simplest solutions of the FutzHugh–Nagumo model have been presented. The asymptotic solutions expressed in terms of Jacobi elliptic functions are found for the standard FutzHugh–Nagumo model. Some exact solutions of the generalized FitzHugh–Nagumo models are obtained with allowance for perturbations in the kinetic equation. The possible application of the solutions obtained in this work to the construction of neural networks. Keywords: neuron, Hodgkin–Hoxley model, FitzHugh–Nagumo model, nonlinear differential equation, Painleve test, exact solutions
Polyanin A.D., Shingareva I.K.
A method of nonlocal transformations is proposed for numerical integration of linear and nonlinear two-point singularly perturbed boundary value problems with a small parameter at the highest derivative. Solutions of such problems are characterized by large gradients in narrow regions, whose structure, characteristic dimensions, and positions in the general case are unknown a priori and are determined in the process of the study. For this reason, the standard numerical methods with a fixed integration step (which should depend on a small parameter) in solving singular problems with a small parameter require an unreasonably large number of grid points and can lead to significant errors. Variable-step adaptive numerical methods face a very difficult problem of adequate organization of the choice of a local grid density in regions with qualitatively different structures of the solution. In this work, a new method has been described for numerical integration of similar problems for second-order ordinary differential equations , which is based on introducing a new nonlocal independent variable ξ, which is related to the original variables x and y by the equation , and the subsequent transformation of the problem under consideration to a boundary value problem for the corresponding system of first-order differential equations. With a suitable choice of the regularizing function g, the proposed method leads to problems that allow the application of standard numerical methods with a fixed step of ξ (in the whole variation range of the independent variable x, including both the boundary-layer region and the outer region). A number of test problems with a small parameter that have simple exact or asymptotic solutions, which are expressed in terms of elementary functions, are presented. Comparison of numerical and exact solutions has shown a high efficiency of the method of nonlocal transformations for solving singular problems with a boundary layer. Keywords: ordinary differential equations with a small parameter, boundary value problems, boundary layers, nonlocal transformations, asymptotic and numerical solutions
The operation regimes of Penning-type cold cathode ion sources in gas-filled neutron tubes for various parameters of pulse-periodic power supply are studied. The results have made it possible to reveal a number of characteristic features of the discharge processes at the ion source activation stage. It has been shown that a stable ignition of discharges is ensured at kilohertz repetition frequencies of supply voltage pulses. The study of the influence of the shape of supply voltage pulses on discharge generation regimes has shown that an increase in the voltage pulse rise time delays the ignition of the discharge and reduces its burning time. This is caused by the additional time costs for exceeding the threshold level of the ignition voltage of the discharge. It has been shown that the discharge ignition dynamics depends on the conditions created on the ion source electrode system between supply voltage pulses. Under the experimental conditions, when the ion sources are triggered with a short polarity reversal of the supply voltage, an increase in the discharge ignition delay time has been observed. It has been detected that the reversed polarity of the voltage on the electrode system during pauses between pulses disturbs the stability of ion source operation. The revealed effects indicate that, when developing neutron generators, it is necessary to use power systems ensuring the formation of unipolar voltage pulses with submicrosecond rise times. Keywords: gas discharge, Penning-type ion source, neutron tube, pulsed power supply
Petrov Yu.P., Kuznetsov N.M., Turetskii S.V., Vlasov P.A., Stovbun S.V.
The kinetics and elementary rate constants k1 of the primary stage of the thermal decomposition of nitromethane behind shock waves at temperatures Т = 990–1400 K, pressures p about 4 bar, and initial material concentration ~ 50–1500 ppm are determined using time-resolved absorption spectroscopic technique. It is found that the major contribution to the kinetics of thermal decomposition of nitromethane comes from an elementary reaction of dissociation via breaking the С–N bond. The contribution of other reactions (in particular, the reaction of isomerization of nitromethane in methyl nitrite) at the initial stages of decomposition is negligible and significantly less than the error of measurements. At high temperatures, the decomposition of nitromethane proceeds exponentially. At low temperatures, the self-acceleration of the decomposition at intermediate stages is observed for the first time. This effect is quantitatively confirmed by numerical simulation in the widest possible ranges of temperatures and pressures using a kinetic scheme including 84 reactions. Taking into account the acceleration factor for the decomposition of nitromethane, Arrhenius dependences are determined in the fall-off pressure region for the values of k1 in the series of experiments with pressures equal to ~ 4, 1.5, 0.5, and 0.28 atm. Keywords: nitromethane, thermal decomposition, self-acceleration of decomposition of nitromethane, roaming-isomerization, initial stage of decomposition of nitromethane
Lozovik Yu.E., Khokhryakov E.I.
The crystallization and melting of mesoscopic clusters of dipole excitons or dipole atoms in a two-dimensional trap controlled by the temperature and dipole moment are studied by Monte Carlo simulation. The pair correlation spectrum, angular dispersion of the relative rotation of cluster shells, and radial dispersion have been considered. The phase diagram of the system and phase transitions in it have been analyzed. In clusters with incommensurable shells, orientational melting of shells first takes place with increasing temperature. Then, radial melting with exchange of particles between shells occurs and, finally, complete disordering occurs. A change in the temperature of orientational melting at the variation of the dipole moment has been found. It has been shown that orientational melting can have one or two stages. An increase in the dipole moment changes one-stage melting to two-stage melting; this behavior correlates with structural phase transitions. Estimate of metabarriers for different relative shell rotations explains mechanism of two stage melting. The melting of two inner shells is a first order structural phase transition, whereas the melting of two outer shells is a second order structural phase transition. Effects of a change in the effective interaction in the system from dipole to Coulomb at the variation of the concentration of particles are also discussed. Keywords: phase transitions, clusters, dipoles, excitons, quantum dots, Monte Carlo method, orientational melting, radial melting, complete melting, order parameter