32 research outputs found
ΠΡΠΎΠ±Π½ΠΎ-Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½Π°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠ΅ΠΏΠ»ΠΎΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΡΡΠΈ ΡΠ΅Π³Π½Π΅ΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»ΠΎΠ² Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ ΠΈΠ½ΡΠ΅Π½ΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π½Π°Π³ΡΠ΅Π²Π°
Ferroelectrics, due a number of characteristics, behave as hereditary materials with fractal structure. To model mathematically the systems with so-called memory effects one can use the fractional time-derivatives. The pyro-electric properties of ferroelectrics arouse interest in developing the fractional-differential approach to simulating heat conductivity process.The present study deals with development and numerical implementation of fractal heat conductivity model for hereditary materials using the concepts of fractional-differential calculus applied to the simulation of intensive heating processes in ferroelectrics.The paper proposes a mathematical model governed through mixed initial-boundary value problem for partial differential equation containing a fractional time-derivative as well as nonlinear temperature dependence on the heat capacity. To solve the problem the computational algorithm was designed which is based on an analog of the Crank β Nicolson finite difference scheme combining with the Grunwald β Letnikov formula for fractional time-derivative approximation. The approximation of Neumann boundary condition is included into the finite difference problem statement using scheme of fictitious mesh points. The total system of linear algebraic equations is solved by sweep method.The designed application program allows one to perform the computer simulation of heat conductivity process in hereditary materials. The model verification was performed for numerical solving test problem with known analytical solution. The results of computational experiments are demonstrated for the example of estimating heat distribution in a typical ferroelectric crystal of TGS (triglycine sulfate) near the temperature of phase transition. The fractional derivative order was approximately evaluated to be ~0.7 at variation of this parameter. We applied the comparison of fractal model implementation results with experimental data related to the time when the ferroelectric crystal is heated to Curie temperature. These findings demonstrate that one needs to use the modified models at the analysis of the field effects arising in hereditary materials.Π‘Π΅Π³Π½Π΅ΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»Ρ ΠΏΠΎ ΡΡΠ΄Ρ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ Π²Π΅Π΄ΡΡ ΡΠ΅Π±Ρ ΠΊΠ°ΠΊ ΡΡΠ΅Π΄ΠΈΡΠ°ΡΠ½ΡΠ΅ ΡΡΠ΅Π΄Ρ Ρ ΡΡΠ°ΠΊΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΡΡΠΊΡΡΡΠΎΠΉ. ΠΠ»Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΈΡΡΠ΅ΠΌ Ρ ΡΡΡΠ΅ΠΊΡΠΎΠΌ ΠΏΠ°ΠΌΡΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡ Π΄ΡΠΎΠ±Π½ΡΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ ΠΏΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ. ΠΠΈΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ²ΠΎΠΉΡΡΠ²Π° ΡΠ΅Π³Π½Π΅ΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΠΊΠΎΠ² ΠΎΠ±ΡΡΠ»Π°Π²Π»ΠΈΠ²Π°ΡΡ ΠΈΠ½ΡΠ΅ΡΠ΅Ρ ΠΊ ΡΠ°Π·Π²ΠΈΡΠΈΡ Π΄ΡΠΎΠ±Π½ΠΎ-Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° ΠΊ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠ΅ΠΏΠ»ΠΎΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΡΡΠΈ.Π Π°Π±ΠΎΡΠ° ΠΏΠΎΡΠ²ΡΡΠ΅Π½Π° ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ΅ ΠΈ ΡΠΈΡΠ»Π΅Π½Π½ΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΡΠ°ΠΊΡΠ°Π»ΡΠ½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠ΅ΠΏΠ»ΠΎΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΡΡΠΈ ΡΡΠ΅Π΄ΠΈΡΠ°ΡΠ½ΡΡ
ΡΡΠ΅Π΄ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠΈΠΉ Π΄ΡΠΎΠ±Π½ΠΎ-Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΈΡΡΠΈΡΠ»Π΅Π½ΠΈΡ Π² ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠΈ ΠΊ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΠΈΠ½ΡΠ΅Π½ΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π½Π°Π³ΡΠ΅Π²Π° ΡΠ΅Π³Π½Π΅ΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»ΠΎΠ².ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠ΅ΠΏΠ»ΠΎΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΡΡΠΈ, ΡΠΎΡΠΌΠ°Π»ΠΈΠ·ΠΎΠ²Π°Π½Π½Π°Ρ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΡΠΌΠ΅ΡΠ°Π½Π½ΠΎΠΉ Π½Π°ΡΠ°Π»ΡΠ½ΠΎ-Π³ΡΠ°Π½ΠΈΡΠ½ΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ Π΄Π»Ρ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Ρ ΡΠ°ΡΡΠ½ΡΠΌΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΠΌΠΈ, Π²ΠΊΠ»ΡΡΠ°ΡΡΠ΅Π³ΠΎ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ Π΄ΡΠΎΠ±Π½ΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΠ° ΠΏΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΠΈ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΡ ΡΠ΅ΠΏΠ»ΠΎΠ΅ΠΌΠΊΠΎΡΡΠΈ ΠΎΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ. Π‘ΠΊΠΎΠ½ΡΡΡΡΠΈΡΠΎΠ²Π°Π½ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½ΡΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π½Π°Π»ΠΎΠ³Π° ΠΊΠΎΠ½Π΅ΡΠ½ΠΎ-ΡΠ°Π·Π½ΠΎΡΡΠ½ΠΎΠΉ ΡΡ
Π΅ΠΌΡ ΠΡΠ°Π½ΠΊΠ° β ΠΠΈΠΊΠΎΠ»ΡΠΎΠ½ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΠΎΡΠΌΡΠ»Ρ ΠΡΡΠ½Π²Π°Π»ΡΠ΄Π° β ΠΠ΅ΡΠ½ΠΈΠΊΠΎΠ²Π° Π΄Π»Ρ Π°ΠΏΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΠΎΠΉ Π΄ΡΠΎΠ±Π½ΠΎΠ³ΠΎ ΠΏΠΎΡΡΠ΄ΠΊΠ° ΠΏΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ. ΠΠΏΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΡ Π³ΡΠ°Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΡΡΠ»ΠΎΠ²ΠΈΡ ΠΠ΅ΠΉΠΌΠ°Π½Π° ΡΡΠΈΡΡΠ²Π°Π΅ΡΡΡ Π² ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΡΡ
ΠΏΡΠΈ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π΅ ΠΎΡ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ ΠΊ ΠΊΠΎΠ½Π΅ΡΠ½ΠΎ-ΡΠ°Π·Π½ΠΎΡΡΠ½ΠΎΠΉ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π²Π²Π΅Π΄Π΅Π½ΠΈΡ ΡΠΈΠΊΡΠΈΠ²Π½ΡΡ
ΡΠ·Π»ΠΎΠ² ΡΠ΅ΡΠΊΠΈ. ΠΡΠΎΠ³ΠΎΠ²Π°Ρ ΡΠΈΡΡΠ΅ΠΌΠ° Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΡΠ΅ΡΠ°Π΅ΡΡΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΏΡΠΎΠ³ΠΎΠ½ΠΊΠΈ.Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° ΠΏΡΠΈΠΊΠ»Π°Π΄Π½Π°Ρ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ°, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠ°Ρ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠ΅ΠΏΠ»ΠΎΠΏΡΠΎΠ²ΠΎΠ΄Π½ΠΎΡΡΠΈ Π΄Π»Ρ ΡΡΠ΅Π΄ΠΈΡΠ°ΡΠ½ΡΡ
ΡΡΠ΅Π΄ Π² ΠΎΠ΄Π½ΠΎΠΉ ΠΈΠ· ΡΠ°ΡΡΠ½ΡΡ
ΠΏΠΎΡΡΠ°Π½ΠΎΠ²ΠΎΠΊ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π° ΠΏΡΠΎΠ²Π΅ΡΠΊΠ° Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎΡΡΠΈ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΡΠΈΡΠ»Π΅Π½Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π° ΡΠ΅ΡΡ-Π·Π°Π΄Π°ΡΠ΅. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠ΄Π΅ΠΌΠΎΠ½ΡΡΡΠΈΡΠΎΠ²Π°Π½Ρ Π΄Π»Ρ ΠΏΡΠΈΠΊΠ»Π°Π΄Π½ΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ β ΠΎΡΠ΅Π½ΠΊΠΈ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ Π² ΠΎΠ±ΡΠ°Π·ΡΠ΅ ΡΠΈΠΏΠΈΡΠ½ΠΎΠ³ΠΎ ΡΠ΅Π³Π½Π΅ΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΠΊΠ° ΡΡΠΈΠ³Π»ΠΈΡΠΈΠ½ΡΡΠ»ΡΡΠ°ΡΠ° ΠΏΡΠΈ ΠΈΠ½ΡΠ΅Π½ΡΠΈΠ²Π½ΠΎΠΌ, ΠΏΠΎ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΊ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ΅ ΡΠ°Π·ΠΎΠ²ΠΎΠ³ΠΎ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π°, ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΌ Π½Π°Π³ΡΠ΅Π²Π΅. ΠΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½Π½ΠΎ ΠΎΡΠ΅Π½Π΅Π½ ΠΏΠΎΡΡΠ΄ΠΎΠΊ Π΄ΡΠΎΠ±Π½ΠΎΠ³ΠΎ Π΄ΠΈΡΡΠ΅ΡΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ (~0.7) Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΡΠ°ΠΊΡΠ°Π»ΡΠ½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ (ΠΏΡΠΈ Π²Π°ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°) Ρ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠΌΠΈ Π΄Π°Π½Π½ΡΠΌΠΈ ΠΏΠΎ ΠΎΡΠ΅Π½ΠΊΠ΅ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Π΄ΠΎΡΡΠΈΠΆΠ΅Π½ΠΈΡ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ ΠΡΡΠΈ. ΠΡΠΎ ΡΠ²ΠΈΠ΄Π΅ΡΠ΅Π»ΡΡΡΠ²ΡΠ΅Ρ ΠΎ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΠΏΡΠΈ Π°Π½Π°Π»ΠΈΠ·Π΅ ΠΏΠΎΠ»Π΅Π²ΡΡ
ΡΡΡΠ΅ΠΊΡΠΎΠ², Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡΡΠΈΡ
Π² ΡΡΠ΅Π΄ΠΈΡΠ°ΡΠ½ΡΡ
ΡΡΠ΅Π΄Π°Ρ
Fractional-Differential Model of Heat Conductivity Process in Ferroelectrics under the Intensive Heating Conditions
Ferroelectrics, due a number of characteristics, behave as hereditary materials with fractal structure. To model mathematically the systems with so-called memory effects one can use the fractional time-derivatives. The pyro-electric properties of ferroelectrics arouse interest in developing the fractional-differential approach to simulating heat conductivity process.The present study deals with development and numerical implementation of fractal heat conductivity model for hereditary materials using the concepts of fractional-differential calculus applied to the simulation of intensive heating processes in ferroelectrics.The paper proposes a mathematical model governed through mixed initial-boundary value problem for partial differential equation containing a fractional time-derivative as well as nonlinear temperature dependence on the heat capacity. To solve the problem the computational algorithm was designed which is based on an analog of the Crank β Nicolson finite difference scheme combining with the Grunwald β Letnikov formula for fractional time-derivative approximation. The approximation of Neumann boundary condition is included into the finite difference problem statement using scheme of fictitious mesh points. The total system of linear algebraic equations is solved by sweep method.The designed application program allows one to perform the computer simulation of heat conductivity process in hereditary materials. The model verification was performed for numerical solving test problem with known analytical solution. The results of computational experiments are demonstrated for the example of estimating heat distribution in a typical ferroelectric crystal of TGS (triglycine sulfate) near the temperature of phase transition. The fractional derivative order was approximately evaluated to be ~0.7 at variation of this parameter. We applied the comparison of fractal model implementation results with experimental data related to the time when the ferroelectric crystal is heated to Curie temperature. These findings demonstrate that one needs to use the modified models at the analysis of the field effects arising in hereditary materials
SPECIAL FEATURES OF FUNCTIONING OF FLAT ROOFS AS THE PLACES FOR SOCIAL COMMUNICATION (on the example of VSUES campus in Vladivostok) / ΠΠ‘ΠΠΠΠΠΠΠ‘Π’Π Π€Π£ΠΠΠ¦ΠΠΠΠΠ ΠΠΠΠΠΠ― ΠΠΠΠ©ΠΠΠΠ ΠΠ ΠΠ Π«Π¨ΠΠ₯ ΠΠΠ ΠΠΠ‘Π’ Π‘ΠΠ¦ΠΠΠΠ¬ΠΠΠ ΠΠΠΠΠ£ΠΠΠΠΠ¦ΠΠ (Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΠΊΠ°ΠΌΠΏΡΡΠ° ΠΠΠ£ΠΠ‘ Π²ΠΎ ΠΠ»Π°Π΄ΠΈΠ²ΠΎΡΡΠΎΠΊΠ΅)
The purpose of the study is to reveal the special features of the flat operable roofs functioning as public spaces based on the example of VSUES campus in Vladivostok city.\ud
The methods of observation, photographic fixation and opinion poll in the form of questioning were adapted for the initial data collection. The methods of analytical architectural phenomenology and structural-semiotic analysis were used for the theoretical research. The symbolic (diagram and drawings) and computer (3d-scenes) simulation was used in experimental-design part of the study.\ud
The informational and recreational spaces, obtained as a result of the roofing surfaces conversion, and their ability to realize the social-communication functions are examined in the article. The role of such spaces as the catalysts of public activity, symbols of the present, signs of the natural and architectural environment unity, indices of the high level of the living environment comfort, concern about the psychological health of society, indices of status and carriers of the institution firm style, means of the knowledge of reality are analyzed.\ud
The theoretical studies and practical experiment make it possible to draw the conclusion about the effectiveness and prospects of the use of flat roofs surfaces as places for social communication, capable to enrich the urban context by the new values and the aesthetical content, to increase the public activity and dynamic density of society. / Π¦Π΅Π»Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠΎΡΡΠΎΠΈΡ Π² ΡΠ°ΡΠΊΡΡΡΠΈΠΈ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΡΡΠ½ΠΊΡΠΈΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΠ»ΠΎΡΠΊΠΈΡ
ΡΠΊΡΠΏΠ»ΡΠ°ΡΠΈΡΡΠ΅ΠΌΡΡ
ΠΊΡΡΡ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΎΠ±ΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΡ
ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ² Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΠΊΠ°ΠΌΠΏΡΡΠ° ΠΠΠ£ΠΠ‘ Π² Π³ΠΎΡΠΎΠ΄Π΅ ΠΠ»Π°Π΄ΠΈΠ²ΠΎΡΡΠΎΠΊΠ΅. \ud
ΠΠ° ΡΡΠ°ΠΏΠ΅ ΡΠ±ΠΎΡΠ° ΠΈΡΡ
ΠΎΠ΄Π½ΡΡ
Π΄Π°Π½Π½ΡΡ
Π² ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ ΠΏΡΠΈΠΌΠ΅Π½ΡΠ»ΠΈΡΡ ΡΠ°ΠΊΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ, ΠΊΠ°ΠΊ Π½Π°Π±Π»ΡΠ΄Π΅Π½ΠΈΠ΅, ΡΠΎΡΠΎΠ³ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠΈΠΊΡΠ°ΡΠΈΡ ΠΈ ΡΠΎΡΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΎΠΏΡΠΎΡ Π² ΡΠΎΡΠΌΠ΅ Π°Π½ΠΊΠ΅ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ. Π ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ°ΡΡΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈΡΡ ΠΌΠ΅ΡΠΎΠ΄Ρ Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π½ΠΎΠΌΠ΅Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π°ΡΡ
ΠΈΡΠ΅ΠΊΡΡΡΡ ΠΈ ΡΡΡΡΠΊΡΡΡΠ½ΠΎ-ΡΠ΅ΠΌΠΈΠΎΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π°. Π ΠΏΡΠΎΠ΅ΠΊΡΠ½ΠΎ-ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΠ°ΡΡΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΎΡΡ ΡΠΈΠΌΠ²ΠΎΠ»ΠΈΡΠ΅ΡΠΊΠΎΠ΅ (ΡΠΈΡΡΠ½ΠΊΠΈ, ΡΡ
Π΅ΠΌΡ ΠΈ ΡΠ΅ΡΡΠ΅ΠΆΠΈ) ΠΈ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ (3D-ΡΡΠ΅Π½Ρ) ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅.\ud
Π ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΡΠ΅ΠΊΠ»Π°ΠΌΠ½ΠΎ-ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΈ ΡΠ΅ΠΊΡΠ΅Π°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π°, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΏΡΠ΅ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠ΅ΠΉ ΠΊΡΠΎΠ²Π»ΠΈ, ΠΈ ΠΈΡ
ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡΡ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°ΡΡ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎ ΡΠΎΡΠΈΠ°Π»ΡΠ½ΠΎ-ΠΊΠΎΠΌΠΌΡΠ½ΠΈΠΊΠ°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡΠ½ΠΊΡΠΈΠΉ. ΠΠ½Π°Π»ΠΈΠ·ΠΈΡΡΠ΅ΡΡΡ ΡΠΎΠ»Ρ ΡΠ°ΠΊΠΈΡ
ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ² ΠΊΠ°ΠΊ ΠΊΠ°ΡΠ°Π»ΠΈΠ·Π°ΡΠΎΡΠΎΠ² ΠΎΠ±ΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ, ΡΠΈΠΌΠ²ΠΎΠ»ΠΎΠ² ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΡΡΠΈ, Π·Π½Π°ΠΊΠΎΠ² Π΅Π΄ΠΈΠ½ΡΡΠ²Π° ΠΏΡΠΈΡΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΈ Π°ΡΡ
ΠΈΡΠ΅ΠΊΡΡΡΠ½ΠΎΠ³ΠΎ ΠΎΠΊΡΡΠΆΠ΅Π½ΠΈΡ, ΠΈΠ½Π΄Π΅ΠΊΡΠΎΠ² Π²ΡΡΠΎΠΊΠΎΠ³ΠΎ ΡΡΠΎΠ²Π½Ρ ΠΊΠΎΠΌΡΠΎΡΡΠ½ΠΎΡΡΠΈ ΡΡΠ΅Π΄Ρ ΠΎΠ±ΠΈΡΠ°Π½ΠΈΡ, Π·Π°Π±ΠΎΡΡ ΠΎ ΠΏΡΠΈΡ
ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΌ Π·Π΄ΠΎΡΠΎΠ²ΡΠ΅ ΠΎΠ±ΡΠ΅ΡΡΠ²Π°, ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΡΡΠ°ΡΡΡΠ° ΠΈ Π½ΠΎΡΠΈΡΠ΅Π»Π΅ΠΉ ΡΠΈΡΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ ΡΡΠΈΠ»Ρ Π·Π°Π²Π΅Π΄Π΅Π½ΠΈΡ, ΡΡΠ΅Π΄ΡΡΠ² ΠΏΠΎΠ·Π½Π°Π½ΠΈΡ Π΄Π΅ΠΉΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ.\ud
ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π½ΠΎΠ΅ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠΉ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ ΡΠ΄Π΅Π»Π°ΡΡ Π²ΡΠ²ΠΎΠ΄ ΠΎΠ± ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΈ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠ΅ΠΉ ΠΏΠ»ΠΎΡΠΊΠΈΡ
ΠΊΡΡΡ ΠΊΠ°ΠΊ ΠΌΠ΅ΡΡ Π΄Π»Ρ ΡΠΎΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΠΊΠΎΠΌΠΌΡΠ½ΠΈΠΊΠ°ΡΠΈΠΈ, ΡΠΏΠΎΡΠΎΠ±Π½ΡΡ
ΠΎΠ±ΠΎΠ³Π°ΡΠΈΡΡ Π³ΠΎΡΠΎΠ΄ΡΠΊΠΎΠΉ ΠΊΠΎΠ½ΡΠ΅ΠΊΡΡ Π½ΠΎΠ²ΡΠΌΠΈ Π·Π½Π°ΡΠ΅Π½ΠΈΡΠΌΠΈ ΠΈ ΡΡΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΡΠΎΠ΄Π΅ΡΠΆΠ°Π½ΠΈΠ΅ΠΌ, ΡΠΏΠΎΡΠΎΠ±ΡΡΠ²ΡΡΡΠΈΡ
ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ ΠΎΠ±ΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΈ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ ΡΠ΅ΠΌ ΡΠ°ΠΌΡΠΌ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ ΡΠΎΡΠΈΡΠΌΠ°\ud
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