Determination of the Exact Orientation of Single-Crystal X-ray Optics from Its Glitch Spectrum and Modeling of Glitches for an Arbitrary Configuration

X-ray optics made of single-crystal materials are widely used at most of the X-ray sources due to the outstanding properties. The main drawback of such optics—the diffraction losses, also known as glitches of intensity in the energy spectrum of the transmitted/diffracted beam. To be able to handle this negative effect, one needs a reliable way to simulate the glitch spectrum in any configuration. Here, we demonstrate the way of precisely determining the crystallographic orientation and unit cell parameters of optical elements just from a small glitch spectrum with the consequent possibility of simulating glitches for any energy.

Один подход к численному решению основного уравнения магнитостатики для конечного цилиндра в произвольном внешнем поле

The magnetostatics direct problem of calculating the resulting magnetic field strength from a homogeneous cylinder of finite dimensions placed in an external magnetic field of arbitrary configuration is considered. With the help of sufficiently voluminous analytical transformations using the basic properties of hypergeometric functions and Legendre functions, the solution of the basic three-dimensional magnetostatic equation for this configuration is reduced to solving of a certain number of systems of three one-dimensional linear integral equations. A simplified form of these systems for special cases of a constant external field and the resulting field on the cylinder axis is obtained.

Unified Methodology for Strength and Stress Analysis of Structural Concrete Members

In this paper, a methodology is presented for determining the stress and strain in structural concrete sections, also, for estimating the ultimate combination of axial forces and bending moments that produce failure. The structural concrete member may have a cross-section with an arbitrary configuration, the concrete region may consist of a set of subregions having different characteristics (i.e., different grades of concretes, or initially identical, but working with different stress-strain diagrams due to the effect of indirect reinforcement or the effect of confinement, etc.). This methodology is considering the tensile strain softening and tension stiffening of concrete in addition to the tension stiffening of steel bars due to the tensile resistance of the surrounding concrete layer. A comparison of experimental and numerical data indicates that the results, obtained based on this methodology, are highly reliable and highly informative.

Application of the Superposition Method for Fault Location in Medium Voltage Networks

Medium-voltage networks are characterized by a long length and high degree of wear. Isolation of a failed network section requires significant time expenditures, a circumstance that makes accurate and fast determination of the fault location a topical problem. In view of specific features of emergency modes in medium voltage networks, the development of precise algorithms for fault location in the case of single and double ground faults involves certain difficulties. The arbitrary configuration of electrical networks, specific neutral grounding conditions, and lack of the possibility to perform multilateral measurements of emergency parameters complicate the development of universal fault location algorithms. In addition, technical solutions are as a rule limited by the need of using one-sided measurements of emergency mode parameters. The considered algorithms for calculating the distance to the fault location involve the use of emergency and normal electric network mode parameters. The proposed algorithms are based on using the superposition method and do not depend on the electrical network topology; they make it possible to decrease the influence of the current distribution pattern in lines with branches, as well as the influence of the load operating conditions on the accuracy of calculating the distance to fault location. The application of the proposed algorithms is justified by the results of simulation and makes it possible to calculate the distance to the fault location in networks with insulated neutral with high accuracy.

DEVELOPMENT OF A MATHEMATICAL MODEL OF TRANSITIONAL PROCESSES IN THE ELECTRICAL NETWORK IN PHASE COORDINATES

Distribution electrical networks of great length are characterized by a high order of the system of equations of electromagnetic transients. To improve the efficiency of modelling such networks, it is necessary to develop formalized procedures that provide automation of both the solution and the formation of systems of equations using modern computer technology. To simplify the development of mathematical models, transformations are used to move from a real three-phase network to other coordinate systems, but this is achieved at the expense of additional restrictions. To solve the problems of choosing and increasing the efficiency of means for limiting currents and overvoltages during transient processes in electrical networks, it is necessary to have a model reflecting a number of features, both of the networks themselves, and of the transient processes occurring in them. This is implemented in a model based on the representation of network elements not by single-phase equivalents, but by equations in phase coordinates. These equations contain the parameters of the network elements (active resistances, own and mutual inductances and capacitances) and the parameters of its mode (currents, voltages, phase powers), corresponding to the real physical parameters of electrical systems. A mathematical model of electromagnetic transient processes in an electrical network in phase coordinates has been developed. Calculation of the transient process when using the implicit method and representing the three-phase elements at the integration step by discrete models makes it possible to reduce the solution of a system of differential equations to multiple formation and solution of a system of equations. The diakoptic method for studying complex systems was developed, which was used to develop a mathematical model of electromagnetic transient processes in a three-phase electrical network. The proposed form of representation of discrete models of three-phase multipoles allows one to formalize both the solution procedure and the procedure for drawing up equations of transient processes for three-phase circuits of electrical networks of arbitrary configuration. Prospects for further research are computational experiments to study electromagnetic transient processes during ground faults in electrical networks of arbitrary configuration with various neutral modes and means of limiting currents and overvoltages.

Study on Arbitrary Direction Navigation System for Autonomous Multirotor with Arbitrary Configuration of Rotors

In this paper, an autonomous aerial robot system with a multirotor mechanism is described, where the robot has an arbitrary configuration of rotors. To construct a navigation system for the arbitrary 3-axis direction, the static constraint conditions are treated as dynamic equilibrium, and the analytical solution of this formulation is obtained with regard to two terms, namely attitude and height control. Moreover, the obtained analytical solution is implemented as a proportional-integral-derivative controller such that the navigation control system is fused with the attitude and height control systems optimally. To confirm the efficacy of this constructed navigation control system, navigation experiments with arbitrary azimuth direction and height are executed for a manufactured trial quadrotor system as an aerial robot and the results are estimated.

Fluid Mixing Nonequilibrium Processes in Industrial Piping Flows

The flow of a multicomponent fluid through a pipeline system of arbitrary configuration is considered. The problem consists in determining the component composition of the fluid for each pipeline of the system based on the values of the concentration of the components throughout the entire set of measuring points, provided that there are no phase transitions. To solve the problem, mathematical models have been developed that, in principle, are suitable for pipeline systems of various functional purposes, the presentation is concretized and carried out in relation to gas transmission systems. The models are stochastic in nature due to measurement errors, which are considered random variables. The solution of the problem is reduced to the optimization of a quadratic function with constraints in the form of equalities and inequalities. The considered mixing processes do not depend on the regime parameters of the fluid flow. The processes are irreversible and non-equilibrium. A criterion is introduced that characterizes the degree of closeness of a multicomponent mixture to an equilibrium state. The criterion is analogous to entropy in thermodynamic processes. A numerical example of calculating the distribution of a three-component mixture is given. The example illustrates the feasibility of the proposed computational procedures and gives an idea of the distribution of the component composition and the change in «entropy» along the directions of pumping of the gas supply system.

Magnetic field evolution time-scales in superconducting neutron stars

ABSTRACT The self-consistent approach to the magnetic field evolution in neutron star (NS) cores, developed recently, is generalized to the case of superfluid and superconducting NSs. Applying this approach to the cold matter of NS cores composed of neutrons, protons, electrons, and muons, we find that, similarly to the case of normal matter, an arbitrary configuration of the magnetic field may result in generation of macroscopic particle velocities, strongly exceeding their diffusive (relative) velocities. This effect substantially accelerates evolution of the magnetic field in the stellar core. An hierarchy of time-scales of such evolution at different stages of NS life is proposed and discussed. It is argued that the magnetic field in the core cannot be considered as frozen or vanishing and that its temporal evolution should affect the observational properties of NSs.