342 research outputs found
The impact of grain boundary character on the size dependence of Bi- crystals
The deformation behavior of metallic single crystals is size dependent, as shown by several studies during the last decade [1]. Nevertheless, real structures exhibit different interfaces like grain, twin or phase boundaries. Due to the possibly higher stresses at the micron scale, the poor availability of dislocation sources and the importance of diffusion in small dimensions the mechanical behavior of samples containing interfaces can considerable differ from bulk materials. Within this study we will show the size scaling behavior of general high angle grain boundaries in copper. The first boundary presented is believed to show extensive dislocation slip transmission at bulk dimensions. The second example acts as perfect obstacle for dislocation slip transfer.
In the talk results from in situ scanning electron microscopy (SEM) and in situ Β΅Laue diffraction will be shown. While the SEM data is used to proof slip transmission, Β΅Laue is probing the occurrence of dislocation pile-ups at the grain boundary. The results show that at low plastic strains the size scaling behavior of single and bi-crystalline samples is identical in cases where the grain size is assumed as the critical length scale [2]. It can therefore be concluded that the initial number and size of dislocation sources is dominating not only the deformation behavior of single crystalline pillars, but also for bi-crystals (at low plastic strains) (see Fig. 1a). Thus, the character of the boundary does not play any role for the mechanical properties at the onset of yield!
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Insights into dislocation grain-boundary interaction by X-ray ΞΌLaue diffraction
The deformation behavior of metallic single crystals is size dependent, as shown by several studies during the last decade. Nevertheless, real structures exhibit different interfaces like grain, twin or phase boundaries. Due to the possibly higher stresses at the micron scale, the poor availability of dislocation sources and the importance of diffusion in small dimensions the mechanical behavior of samples containing interfaces can considerable differ from bulk material.
In the talk we show the first in situ Β΅Laue compression experiments on micron sized, bi-crystalline samples. Three different grain-boundary types will be presented and discussed (i) Large Angle grain Boundaries (LAGBs) acting as strong obstacle for dislocation slip transfer; (ii) LAGBs allowing for easy slip transfer and (iii) coherent sigma 3 twin-boundaries. The talk will focus on pile-up of dislocations, slip transfer mechanisms, storage of dislocations and dislocation networks at the LAGB
A METHOD FOR CALCULATING MECHANICAL CHARACTERISTICS OF INDUCTION MOTORS WITH SQUIRREL-CAGE ROTOR
Purpose. Development of a method for calculating mechanical characteristics of induction motors, taking into consideration saturation of the magnetic path and displacement of the current in the rotor bars. Methodology. The algorithm is based on calculating the steady-state mode of induction motor operation for a set slip, described by a system of non-linear algebraic equations of electrical equilibrium, whereas the mechanical characteristic is evaluated as a set of steady-state modes using parameter continuation method. The idea of the steady-state mode calculation consists in determining vectors of currents and flux linkages of the motor circuits, using which makes it possible to evaluate the electromagnetic torque, active and reactive powers, etc. Results. The study resulted in the development of a method and algorithm for calculating static characteristics of induction motors, which allows looking into the effect of different laws of voltage regulation on the mechanical characteristics, depending on the frequency change. Originality. An algorithm for calculating mechanical characteristics of the squirrel-cage induction motor was developed based on the mathematical model of the induction motor in which electromagnetic parameters are calculated using real saturation curves for the main magnetic flux and leakage fluxes, and displacement of the current in the rotor bars is evaluated by presenting the rotor winding as a multi-layer structure. Applying the transformation of the electrical equilibrium equations into the orthogonal axes enabled a significant reduction of calculation volume without impairing the accuracy of the results. Practical value. The developed algorithm allows studying the effect of different laws of scalar regulation of the voltage on the mechanical characteristics of the induction motor in order to obtain the necessary torque-speed curves for their optimization. It can be used for programming frequency converters
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Transboundary Water Institutions in Developing Countries : A Case Study in Afghanistan
This study addresses the questions: 1) What kind of transboundary water management institution is needed for Afghanistan; and 2) what expertise is required for the institution and which stakeholders should be involved?
The establishment of a transboundary water resources management institution/unit is an essential step for Afghanistan in order to tackle the transboundary waters issue with its co-riparian states. The research also indicated the primary challenges and obstacles (ranging from political matters to technical issues) that a developing country like Afghanistan should anticipate while creating a transboundary waters institution.
This study also focused on the perceived risks of cooperation over transboundary water resources from the Afghan standpoint. Furthermore, it reviewed the experience of cooperation between Afghanistan and Iran over the Helmand waters negotiation in 1973. To address the aforementioned questions, I Interviewed transboundary water experts of Afghanistan, applied the risk and opportunities to cooperation framework, used the available literature and secondary data on the topic, and used the situation mapping tool for the Helmand Basin case.
At present, lack of technical knowledge, data gaps, weak bargaining and negotiation skills relative to co-riparian states, lack of public support to transboundary waters negotiations β due to lack of awareness of the topic - doubts on faithfulness of co-riparian states on delivering benefits, and the existence of various stakeholders of transboundary waters in the Afghan government are the main concerns. On whether Afghanistan should cooperate or not, the study found that none of the interviewees opposed transboundary water negotiations. However, there were two camps regarding the timing of dialogues with co-riparians. The first group of participants was in favor of dialogue initiation with co-riparian states for now, and the eventual negotiation of water treaties or agreements in the future. The second group opposes current negotiations - this camp wants Afghanistanβs government to start preparing and enhancing its technical knowledge and capacity, bargaining skills, and institutional arrangements for future negotiations.
Study results showed existing political will toward transboundary water cooperation and the availability of abundant funding from the donor agencies, as well as from the government of Afghanistan to transboundary waters. Recommendations were made for the design and structure of a transboundary water resources management unit, believed to be the first of its kind in the world. In addition, this study identified the perceived risks to cooperation, and, based on those identified risks, offered risk reduction strategies as well
KOPEKΠ¦IΠ― OΠ'ΠMΠ£AMHIOTΠΠ§HOΠ Π ΠΠΠΠΠ Π£ BAΠITHΠΠ₯ ΠΠ Π IΠIOΠATΠΠ§HOMΠ£ MAΠOBOΠΠI.
It was estabiished that theΒ deveiopment of idiopathic oiigohydramnios important roie of increasing piasma osmoiarity mother. Hidratatsiyna therapy can not oniyincrease the amount of amniotic fiuid butaiso improve the iife support systems of the fetus.Π£cΡaΠ½oΠ²Π»Π΅Π½o, ΡΡΠΎ Π² ΡΠ°Π·Π²ΠΈΡΠΈΠΈ ΠΈΠ΄ΠΈoΠΏaΡΠΈΡΠ΅cΠΊoΠ³o ΠΌΠ°Π»ΠΎΠ²ΠΎΠ΄ΠΈΡ Π²Π°ΠΆΠ½Π°Ρ ΡΠΎΠ»Ρ ΠΏΡΠΈΠ½Π°Π΄Π»Π΅ΠΆΠΈΡ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ ocΠΌoΠ»ΡpΠ½ocΡΠΈ ΠΏΠ»Π°Π·ΠΌΡ ΠΊΡΠΎΠ²ΠΈΒ ΠΌΠ°ΡΠ΅ΡΠΈ. ΠΠΈΠ΄ΡΠ°ΡΠ°ΡΠΈΠΎΠ½Π½Π°Ρ ΡΠ΅ΡΠ°ΠΏΠΈΡ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π½Π΅ ΡΠΎΠ»ΡΠΊΠΎ ΡΠ²Π΅Π»ΠΈΡΠΈΡΡ ΠΎΠ±ΡΠ΅ΠΌ Π°ΠΌΠ½ΠΈΠΎΡΠΈΡΠ΅^ΠΎΠΉ ΠΆΠΈΠ΄ΠΊΠΎΡΡΠΈ, Π½ΠΎ ΠΈ ΡΠ»ΡΡΡΠΈΡΡΒ ΠΆΠΈΠ·Π½Π΅ΠΎΠ±Π΅ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΠΏΠ»ΠΎΠ΄Π°.Β ΠΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΠΎ Π² ΡΠΎΠ·Π²ΠΈΡΠΊΡΒ ΡΠ΄ΡΠΎΠΏΠ°ΡΠΈΡΠ½ΠΎΠ³ΠΎ ΠΌΠ°Π»ΠΎΠ²ΠΎΠ΄Π΄Ρ Π²Π°ΠΆΠ»ΠΈΠ²Π° ΡΠΎΠ»Ρ Π½Π°Π»Π΅ΠΆΠΈΡΡ ΠΏΡΠ΄Π²ΠΈΡΠ΅Π½Π½Ρ ocΠΌoΠ»ΡpΠ½ocΡi ΠΏΠ»Π°Π·ΠΌΠΈ ΠΊΡΠΎΠ²Ρ ΠΌΠ°ΡΠ΅ΡΡ. ΠΡΠ΄ΡΠ°ΡΠ°ΡΡΠΉΠ½Π° ΡΠ΅ΡΠ°ΠΏΡΡ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡΒ Π½Π΅ ΡΡΠ»ΡΠΊΠΈ Π·Π±ΡΠ»ΡΡΠΈΡΠΈ ΠΎΠ±'ΡΠΌ Π°ΠΌΠ½ΡΠΎΡΠΈΡΠ½ΠΎΡ ΡΡΠ΄ΠΈΠ½ΠΈ Π°Π»Π΅ ΠΉ ΠΏΠΎΠΊΡΠ°ΡΠΈΡΠΈ ΠΆΠΈΡΡΡΠ·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ ΠΏΠ»ΠΎΠ΄Π°
The innovative component of the system of economic security of Ukrainian transportation industry enterprises
Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡ Π°ΠΊΡΠΈΠ²ΠΈΠ·Π°ΡΠΈΠΈ ΠΈΠ½Π½ΠΎΠ²Π°ΡΠΈΠΎΠ½Π½ΠΎΠΉ Π΄Π΅ΡΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ Π² ΡΡΠ°Π½ΡΠΏΠΎΡΡΠ½ΠΎΠΉ ΠΎΡΡΠ°ΡΠ»ΠΈ. ΠΡΡΠ»Π΅Π΄ΡΡΡΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΊΠ»Π°ΡΡΠ΅ΡΠ½ΠΎΠΉ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΠΈ Π² ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ ΠΏΡΠ΅Π΄ΠΏΡΠΈΡΡΠΈΠΉ ΡΡΠ°Π½ΡΠΏΠΎΡΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ° Π·Π° ΡΡΠ΅Ρ Π°ΠΊΡΠΈΠ²ΠΈΠ·Π°ΡΠΈΠΈ ΠΈΠ½Π½ΠΎΠ²Π°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ°Π·Π²ΠΈΡΠΈΡ
ΠΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΈ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ Π°ΡΠΈΠ½Ρ ΡΠΎΠ½Π½ΠΎΠ³ΠΎ Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Ρ ΠΏΡΠΈ ΠΏΠΈΡΠ°Π½ΠΈΠΈ ΠΎΡ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ° ΡΠΎΠΊΠ°
. Methods and mathematical models for studying the modes and characteristics of the three-phase squirrel-cage induction motor with the power supplied to the stator winding from the current source have been developed. The specific features of the algorithms for calculating transients, steady-state modes and static characteristics are discussed. The results of the calculation of the processes and characteristics of induction motors with the power supply from the current source and the voltage source are compared. Steady-state and dynamic modes cannot be studied with a sufficient adequacy based on the known equivalent circuits; this requires using dynamic parameters, which are the elements of the Jacobi matrix of the system of equations of the electromechanical equilibrium. In the mathematical model, the state equations of the stator and rotor circuits are written in the fixed two-phase coordinate system. The transients are described by the system of differential equations of electrical equilibrium of the transformed circuits of the motor and the equation of the rotor motion and the steady-state modes by the system of algebraic equation. The developed algorithms are based on the mathematical model of the motor in which the magnetic path saturation and skin effect in the squirrel-cage bars are taken into consideration. The magnetic path saturation is accounted for by using the real characteristics of magnetizing by the main magnetic flux and leakage fluxes of the stator and rotor windings. Based on them, the differential inductances are calculated, which are the elements of the Jacobi matrix of the system of equations describing the dynamic modes and static characteristic. In order to take into account the skin effect in the squirrel-cage rotor, each bar along with the squirrel-cage rings is divided height-wise into several elements. As a result, the mathematical model considers the equivalent circuits of the rotor with different parameters which are connected by mutual inductance. The non-linear system of algebraic equations of electrical equilibrium describing the steady-state modes is solved by the parameter continuation method. To calculate the static characteristics, the differential method combined with the Newtonβs Iterative refinement is used.Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Ρ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΈ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π΄Π»Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΠΆΠΈΠΌΠΎΠ² ΠΈ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΡΡΠ΅Ρ
ΡΠ°Π·Π½ΠΎΠ³ΠΎ Π°ΡΠΈΠ½Ρ
ΡΠΎΠ½Π½ΠΎΠ³ΠΎ Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Ρ Ρ ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡΡΡΠΌ ΡΠΎΡΠΎΡΠΎΠΌ ΠΏΡΠΈ ΠΏΠΈΡΠ°Π½ΠΈΠΈ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ ΡΡΠ°ΡΠΎΡΠ° ΠΎΡ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ° ΡΠΎΠΊΠ°. ΠΠ·Π»ΠΎΠΆΠ΅Π½Ρ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΡΠΎΠ·Π΄Π°Π½Π½ΡΡ
Π½Π° ΠΈΡ
ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΠ°ΡΡΠ΅ΡΠ° ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π½ΡΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ², ΡΡΡΠ°Π½ΠΎΠ²ΠΈΠ²ΡΠΈΡ
ΡΡ ΡΠ΅ΠΆΠΈΠΌΠΎΠ² ΠΈ ΡΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ. ΠΡΠΈΠ²Π΅Π΄Π΅Π½ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΡΠ°ΡΡΠ΅ΡΠ° ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΠΈ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ Π°ΡΠΈΠ½Ρ
ΡΠΎΠ½Π½ΡΡ
Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Π΅ΠΉ ΠΏΡΠΈ ΠΏΠΈΡΠ°Π½ΠΈΠΈ ΠΎΡ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ° ΡΠΎΠΊΠ° ΠΈ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ° Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ. ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΡΡΠ°Π½ΠΎΠ²ΠΈΠ²ΡΠΈΡ
ΡΡ ΠΈ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅ΠΆΠΈΠΌΠΎΠ² Π½Π΅ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΠΎΡΡΡΠ΅ΡΡΠ²Π»Π΅Π½ΠΎ Ρ Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎΠΉ Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎΡΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
ΡΡ
Π΅ΠΌ Π·Π°ΠΌΠ΅ΡΠ΅Π½ΠΈΡ ΠΈ ΡΡΠ΅Π±ΡΠ΅Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², ΡΠ²Π»ΡΡΡΠΈΡ
ΡΡ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠ°ΠΌΠΈ ΠΌΠ°ΡΡΠΈΡΡ Π―ΠΊΠΎΠ±ΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠΈΡ. Π ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΠΊΠΎΠ½ΡΡΡΠΎΠ² ΡΡΠ°ΡΠΎΡΠ° ΠΈ ΡΠΎΡΠΎΡΠ° ΡΠΎΡΡΠ°Π²Π»Π΅Π½Ρ Π² Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΡΠ°Π·Π½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΠ΅ ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°Ρ. ΠΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π½ΡΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΡ ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΡΡ ΡΠΈΡΡΠ΅ΠΌΠΎΠΉ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠΈΡ ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½Π½ΡΡ
ΠΊΠΎΠ½ΡΡΡΠΎΠ² Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Ρ ΠΈ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ΠΌ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ ΡΠΎΡΠΎΡΠ°, Π° ΡΡΡΠ°Π½ΠΎΠ²ΠΈΠ²ΡΠΈΠ΅ΡΡ ΡΠ΅ΠΆΠΈΠΌΡ β ΡΠΈΡΡΠ΅ΠΌΠΎΠΉ Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ. Π ΠΎΡΠ½ΠΎΠ²Ρ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π½ΡΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½Π° ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Ρ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΡΠΈΡΡΠ²Π°ΡΡΡΡ Π½Π°ΡΡΡΠ΅Π½ΠΈΠ΅ ΠΌΠ°Π³Π½ΠΈΡΠΎΠΏΡΠΎΠ²ΠΎΠ΄Π° ΠΈ ΡΠ²Π»Π΅Π½ΠΈΠ΅ ΡΠΊΠΈΠ½-ΡΡΡΠ΅ΠΊΡΠ° Π² ΡΡΠ΅ΡΠΆΠ½ΡΡ
ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡΡΠΎΠΉ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ. ΠΠ»Ρ ΡΡΠ΅ΡΠ° Π½Π°ΡΡΡΠ΅Π½ΠΈΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΡΠ΅Π°Π»ΡΠ½ΡΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ Π½Π°ΠΌΠ°Π³Π½ΠΈΡΠΈΠ²Π°Π½ΠΈΡ ΠΎΡΠ½ΠΎΠ²Π½ΡΠΌ ΠΌΠ°Π³Π½ΠΈΡΠ½ΡΠΌ ΠΏΠΎΡΠΎΠΊΠΎΠΌ ΠΈ ΠΏΠΎΡΠΎΠΊΠ°ΠΌΠΈ ΡΠ°ΡΡΠ΅ΡΠ½ΠΈΡ ΠΎΠ±ΠΌΠΎΡΠΎΠΊ ΡΡΠ°ΡΠΎΡΠ° ΠΈ ΡΠΎΡΠΎΡΠ°. ΠΠ° ΠΈΡ
ΠΎΡΠ½ΠΎΠ²Π΅ Π²ΡΡΠΈΡΠ»ΡΡΡΡΡ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠ΅ ΠΈΠ½Π΄ΡΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ²Π»ΡΡΡΡΡ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠ°ΠΌΠΈ ΠΌΠ°ΡΡΠΈΡΡ Π―ΠΊΠΎΠ±ΠΈ ΡΠΈΡΡΠ΅ΠΌ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ, ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΠΈΡ
Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΆΠΈΠΌΡ ΠΈ ΡΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ. Π‘ ΡΠ΅Π»ΡΡ ΡΡΠ΅ΡΠ° ΡΠΊΠΈΠ½-ΡΡΡΠ΅ΠΊΡΠ° Π² ΠΎΠ±ΠΌΠΎΡΠΊΠ΅ ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡΡΠΎΠ³ΠΎ ΡΠΎΡΠΎΡΠ° ΠΊΠ°ΠΆΠ΄ΡΠΉ ΡΡΠ΅ΡΠΆΠ΅Π½Ρ Π²ΠΌΠ΅ΡΡΠ΅ Ρ ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΡΠΊΠ°ΡΡΠΈΠΌΠΈ ΠΊΠΎΠ»ΡΡΠ°ΠΌΠΈ ΡΠ°Π·Π±ΠΈΠ²Π°Π΅ΡΡΡ ΠΏΠΎ Π²ΡΡΠΎΡΠ΅ Π½Π° Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ². Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ Π² ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠ½ΡΠ΅ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ ΡΠΎΡΠΎΡΠ° Ρ ΡΠ°Π·Π½ΡΠΌΠΈ ΠΏΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ, ΠΌΠ΅ΠΆΠ΄Ρ ΠΊΠΎΡΠΎΡΡΠΌΠΈ ΡΡΡΠ΅ΡΡΠ²ΡΡΡ Π²Π·Π°ΠΈΠΌΠΎΠΈΠ½Π΄ΡΠΊΡΠΈΠ²Π½ΡΠ΅ ΡΠ²ΡΠ·ΠΈ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠΈΡ, ΠΊΠΎΡΠΎΡΠΎΠΉ ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΡΡ ΡΡΡΠ°Π½ΠΎΠ²ΠΈΠ²ΡΠΈΠ΅ΡΡ ΡΠ΅ΠΆΠΈΠΌΡ, Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΏΡΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΈΡ ΠΏΠΎ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡ. ΠΠ»Ρ ΡΠ°ΡΡΠ΅ΡΠ° ΡΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ Π² ΡΠΎΡΠ΅ΡΠ°Π½ΠΈΠΈ Ρ ΠΈΡΠ΅ΡΠ°ΡΠΈΠΎΠ½Π½ΡΠΌ ΡΡΠΎΡΠ½Π΅Π½ΠΈΠ΅ΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΡΡΡΠΎΠ½Π°
Orientation dependence of dislocation transmission through twin-boundaries studied by in situ ΞΌLaue diffraction
It is well known that the grain boundaries (GBs) act as a barrier for dislocation motion (Clark 1992), leading to the well-known strength increase with reduced grain size, as explained by the Hall-Petch relation. Unfortunately the strength increase often leads to a reduction of ductility, except one example: Nano-twinned microstructures. The twin-boundary (TB) dislocation interaction is still not thoroughly understood (Imrich 2014, Gumbsch 2006).
Recent developments in deforming micron sized samples on synchrotron beamlines allow to study the interplay of the single dislocation with a specific grain boundary. In present work we conduct in situ compression on micron-sized copper specimens with differently oriented coherent Ξ£3 twin boundaries. The samples were grown by the Bridgman method and subsequently fabricated using FIB milling. The in situ Laue microdiffraction experiments (Β΅Laue) were performed on BM32 at the ESRF synchrotron light source. The experiments allow a clear insight into the stress state, and the density and type of geometrically necessary dislocations stored inside the material during compression. The complementary in situ scanning electron microscope (SEM) experiments further allow to analyze slip transfer by slip step analysis.
The discussion will concentrate on the dislocation transmission mechanism through the TB and the necessity to store dislocations in some specific loading directions as against others
Π£Π‘Π’ΠΠΠΠΠΠΠ¨ΠΠΠ‘Π― Π ΠΠΠΠΠ« Π Π‘Π’ΠΠ’ΠΠ§ΠΠ‘ΠΠΠ Π₯ΠΠ ΠΠΠ’ΠΠ ΠΠ‘Π’ΠΠΠ Π’Π ΠΠ₯Π€ΠΠΠΠΠΠ ΠΠ‘ΠΠΠ₯Π ΠΠΠΠΠΠ ΠΠΠΠΠΠ’ΠΠΠ― ΠΠ Π ΠΠΠ’ΠΠΠΠ ΠΠ’ ΠΠΠΠΠ€ΠΠΠΠΠ Π‘ΠΠ’Π
A mathematical model is developed to study the operation of three-phase asynchronous motor with squirrel-cage rotor when the stator winding is powered from a single phase network. To create a rotating magnetic field one of the phases is fed through the capacitor. Due to the asymmetry of power feed not only transients, but the steady-state regimes are dynamic, so they are described by differential equations in any coordinate system. Their study cannot be carried out with sufficient adequacy on the basis of known equivalent circuits and require the use of dynamic parameters. In the mathematical model the state equations of the circuits of the stator and rotor are composed in the stationary three phase coordinate system. Calculation of the established mode is performed by solving the boundary problem that makes it possible to obtain the coordinate dependences over the period, without calculation of the transient process. In order to perform it, the original nonlinear differential equations are algebraized by approximating the variables with the use of cubic splines. The resulting nonlinear system of algebraic equations is a discrete analogue of the initial system of differential equations. It is solved by parameter continuation method. To calculate the static characteristics as a function of a certain variable, the system is analytically differentiated, and then numerically integrated over this variable. In the process of integration, Newton's refinement is performed at each step or at every few steps, making it possible to implement the integration in just a few steps using Euler's method. Jacobi matrices in both cases are the same. To account for the current displacement in the rods of the squirrel-cage rotor, each of them, along with the squirrel-cage rings, is divided in height into several elements. This results in several squirrel-cage rotor windings which are represented by three-phase windings with magnetic coupling between them.Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ Π΄Π»Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ°Π±ΠΎΡΡ ΡΡΠ΅Ρ
ΡΠ°Π·Π½ΠΎΠ³ΠΎ Π°ΡΠΈΠ½Ρ
ΡΠΎΠ½Π½ΠΎΠ³ΠΎ Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»Ρ Ρ ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡΡΡΠΌ ΡΠΎΡΠΎΡΠΎΠΌ ΠΏΡΠΈ ΠΏΠΈΡΠ°Π½ΠΈΠΈ ΠΎΠ±ΠΌΠΎΡΠΊΠΈ ΡΡΠ°ΡΠΎΡΠ° ΠΎΡ ΠΎΠ΄Π½ΠΎΡΠ°Π·Π½ΠΎΠΉ ΡΠ΅ΡΠΈ. ΠΠ»Ρ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ Π²ΡΠ°ΡΠ°ΡΡΠ΅Π³ΠΎΡΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ ΠΎΠ΄Π½Π° ΠΈΠ· ΡΠ°Π· ΠΏΠΈΡΠ°Π΅ΡΡΡ ΡΠ΅ΡΠ΅Π· ΠΊΠΎΠ½Π΄Π΅Π½ΡΠ°ΡΠΎΡ. ΠΡΠ»Π΅Π΄ΡΡΠ²ΠΈΠ΅ Π½Π΅ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΠΈ Π½Π΅ ΡΠΎΠ»ΡΠΊΠΎ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π½ΡΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΡ, Π½ΠΎ ΠΈ ΡΡΡΠ°Π½ΠΎΠ²ΠΈΠ²ΡΠΈΠ΅ΡΡ ΡΠ΅ΠΆΠΈΠΌΡ ΡΠ²Π»ΡΡΡΡΡ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ, ΠΏΠΎΡΡΠΎΠΌΡ Π² Π»ΡΠ±ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΠ΅ ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°Ρ ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΡΡ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠΌΠΈ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡΠΌΠΈ. ΠΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π΅ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ Ρ Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎΠΉ Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎΡΡΡΡ ΠΎΡΡΡΠ΅ΡΡΠ²Π»Π΅Π½ΠΎ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
ΡΡ
Π΅ΠΌ Π·Π°ΠΌΠ΅ΡΠ΅Π½ΠΈΡ ΠΈ ΡΡΠ΅Π±ΡΠ΅Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ². Π ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΠΊΠΎΠ½ΡΡΡΠΎΠ² ΡΡΠ°ΡΠΎΡΠ° ΠΈ ΡΠΎΡΠΎΡΠ° ΡΠΎΡΡΠ°Π²Π»Π΅Π½Ρ Π² Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ ΡΡΠ΅Ρ
ΡΠ°Π·Π½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΠ΅ ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°Ρ. Π Π°ΡΡΠ΅Ρ ΡΡΡΠ°Π½ΠΎΠ²ΠΈΠ²ΡΠ΅Π³ΠΎΡΡ ΡΠ΅ΠΆΠΈΠΌΠ° Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ ΠΏΡΡΠ΅ΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΊΡΠ°Π΅Π²ΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ, ΡΡΠΎ Π΄Π°Π΅Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΏΠΎΠ»ΡΡΠΈΡΡ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°Ρ Π½Π° ΠΏΠ΅ΡΠΈΠΎΠ΄Π΅, Π½Π΅ ΠΏΡΠΈΠ±Π΅Π³Π°Ρ ΠΊ ΡΠ°ΡΡΠ΅ΡΡ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΏΡΠΎΡΠ΅ΡΡΠ°. ΠΠ»Ρ ΡΡΠΎΠ³ΠΎ ΠΈΡΡ
ΠΎΠ΄Π½ΡΠ΅ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΠ΅ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠ΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Π°Π»Π³Π΅Π±ΡΠ°ΠΈΠ·ΠΈΡΡΡΡΡΡ ΠΏΡΡΠ΅ΠΌ Π°ΠΏΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΠΈ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΠΊΡΠ±ΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΡΠΏΠ»Π°ΠΉΠ½Π°ΠΌΠΈ. ΠΠΎΠ»ΡΡΠ΅Π½Π½Π°Ρ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½Π°Ρ ΡΠΈΡΡΠ΅ΠΌΠ° Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΡΠ²Π»ΡΠ΅ΡΡΡ Π΄ΠΈΡΠΊΡΠ΅ΡΠ½ΡΠΌ Π°Π½Π°Π»ΠΎΠ³ΠΎΠΌ ΠΈΡΡ
ΠΎΠ΄Π½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ. ΠΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΏΡΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΈΡ ΠΏΠΎ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡ. ΠΠ»Ρ ΡΠ°ΡΡΠ΅ΡΠ° ΡΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ ΠΊΠ°ΠΊ ΡΡΠ½ΠΊΡΠΈΠΈ Π½Π΅ΠΊΠΎΡΠΎΡΠΎΠΉ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ Π΄Π°Π½Π½Π°Ρ ΡΠΈΡΡΠ΅ΠΌΠ° Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΡΡΠ΅ΡΡΡ Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈ, Π° Π·Π°ΡΠ΅ΠΌ ΠΈΠ½ΡΠ΅Π³ΡΠΈΡΡΠ΅ΡΡΡ ΡΠΈΡΠ»Π΅Π½Π½ΡΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΏΠΎ ΡΡΠΎΠΉ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ. Π ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΠΈΠ½ΡΠ΅Π³ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π° ΠΊΠ°ΠΆΠ΄ΠΎΠΌ ΡΠ°Π³Π΅ ΠΈΠ»ΠΈ ΡΠ΅ΡΠ΅Π· Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΡΠ°Π³ΠΎΠ² ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΡΡ ΡΡΠΎΡΠ½Π΅Π½ΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΡΡΡΠΎΠ½Π°, ΡΡΠΎ Π΄Π°Π΅Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΎΡΡΡΠ΅ΡΡΠ²ΠΈΡΡ ΠΈΠ½ΡΠ΅Π³ΡΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΠΉΠ»Π΅ΡΠ° Π·Π° Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΡΠ°Π³ΠΎΠ². ΠΠ°ΡΡΠΈΡΡ Π―ΠΊΠΎΠ±ΠΈ Π² ΠΎΠ±ΠΎΠΈΡ
ΡΠ»ΡΡΠ°ΡΡ
ΡΠΎΠ²ΠΏΠ°Π΄Π°ΡΡ. ΠΠ»Ρ ΡΡΠ΅ΡΠ° Π²ΡΡΠ΅ΡΠ½Π΅Π½ΠΈΡ ΡΠΎΠΊΠ° Π² ΡΡΠ΅ΡΠΆΠ½ΡΡ
ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡΡΠΎΠ³ΠΎ ΡΠΎΡΠΎΡΠ° ΠΊΠ°ΠΆΠ΄ΡΠΉ ΡΡΠ΅ΡΠΆΠ΅Π½Ρ Π²ΠΌΠ΅ΡΡΠ΅ Ρ ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΡΠΊΠ°ΡΡΠΈΠΌΠΈ ΠΊΠΎΠ»ΡΡΠ°ΠΌΠΈ ΡΠ°Π·Π±ΠΈΠ²Π°Π΅ΡΡΡ ΠΏΠΎ Π²ΡΡΠΎΡΠ΅ Π½Π° Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ². Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ Π½Π° ΡΠΎΡΠΎΡΠ΅ ΠΏΠΎΠ»ΡΡΠ°Π΅ΠΌ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΠΊΠΎΡΠΎΡΠΊΠΎΠ·Π°ΠΌΠΊΠ½ΡΡΡΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ, ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠΈΡΡΡΡΠΈΡ
ΡΡ ΡΡΠ΅Ρ
ΡΠ°Π·Π½ΡΠΌΠΈ ΠΎΠ±ΠΌΠΎΡΠΊΠ°ΠΌΠΈ, ΠΌΠ΅ΠΆΠ΄Ρ ΠΊΠΎΡΠΎΡΡΠΌΠΈ ΡΡΡΠ΅ΡΡΠ²ΡΡΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΡΠ΅ ΡΠ²ΡΠ·ΠΈ
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