32 research outputs found

    Π”Ρ€ΠΎΠ±Π½ΠΎ-Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½Π°Ρ модСль процСсса тСплопроводности сСгнСтоэлСктричСских ΠΌΠ°Ρ‚Π΅Ρ€ΠΈΠ°Π»ΠΎΠ² Π² условиях интСнсивного Π½Π°Π³Ρ€Π΅Π²Π°

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    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 – Nicolson finite difference scheme combining with the Grunwald – 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.БСгнСтоэлСктричСскиС ΠΌΠ°Ρ‚Π΅Ρ€ΠΈΠ°Π»Ρ‹ ΠΏΠΎ ряду характСристик Π²Π΅Π΄ΡƒΡ‚ сСбя ΠΊΠ°ΠΊ эрСдитарныС срСды с Ρ„Ρ€Π°ΠΊΡ‚Π°Π»ΡŒΠ½ΠΎΠΉ структурой. Для матСматичСского модСлирования систСм с эффСктом памяти ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΡŽΡ‚ Π΄Ρ€ΠΎΠ±Π½ΡƒΡŽ ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡƒΡŽ ΠΏΠΎ Π²Ρ€Π΅ΠΌΠ΅Π½ΠΈ. ΠŸΠΈΡ€ΠΎΡΠ»Π΅ΠΊΡ‚Ρ€ΠΈΡ‡Π΅ΡΠΊΠΈΠ΅ свойства сСгнСтоэлСктриков ΠΎΠ±ΡƒΡΠ»Π°Π²Π»ΠΈΠ²Π°ΡŽΡ‚ интСрСс ΠΊ Ρ€Π°Π·Π²ΠΈΡ‚ΠΈΡŽ Π΄Ρ€ΠΎΠ±Π½ΠΎ-Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ…ΠΎΠ΄Π° ΠΊ ΠΌΠΎΠ΄Π΅Π»ΠΈΡ€ΠΎΠ²Π°Π½ΠΈΡŽ процСсса тСплопроводности.Π Π°Π±ΠΎΡ‚Π° посвящСна Ρ€Π°Π·Ρ€Π°Π±ΠΎΡ‚ΠΊΠ΅ ΠΈ числСнной Ρ€Π΅Π°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ Ρ„Ρ€Π°ΠΊΡ‚Π°Π»ΡŒΠ½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ процСсса тСплопроводности эрСдитарных срСд Π½Π° основС ΠΊΠΎΠ½Ρ†Π΅ΠΏΡ†ΠΈΠΉ Π΄Ρ€ΠΎΠ±Π½ΠΎ-Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½ΠΎΠ³ΠΎ исчислСния Π² ΠΏΡ€ΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠΈ ΠΊ описанию процСссов интСнсивного Π½Π°Π³Ρ€Π΅Π²Π° сСгнСтоэлСктричСских ΠΌΠ°Ρ‚Π΅Ρ€ΠΈΠ°Π»ΠΎΠ².ΠŸΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½Π° матСматичСская модСль процСсса тСплопроводности, формализованная с ΠΏΠΎΠΌΠΎΡ‰ΡŒΡŽ смСшанной Π½Π°Ρ‡Π°Π»ΡŒΠ½ΠΎ-Π³Ρ€Π°Π½ΠΈΡ‡Π½ΠΎΠΉ Π·Π°Π΄Π°Ρ‡ΠΈ для уравнСния с частными ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄Π½Ρ‹ΠΌΠΈ, Π²ΠΊΠ»ΡŽΡ‡Π°ΡŽΡ‰Π΅Π³ΠΎ ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡƒΡŽ Π΄Ρ€ΠΎΠ±Π½ΠΎΠ³ΠΎ порядка ΠΏΠΎ Π²Ρ€Π΅ΠΌΠ΅Π½ΠΈ ΠΈ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡƒΡŽ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡ‚ΡŒ тСплоСмкости ΠΎΡ‚ Ρ‚Π΅ΠΌΠΏΠ΅Ρ€Π°Ρ‚ΡƒΡ€Ρ‹. Бконструирован Π²Ρ‹Ρ‡ΠΈΡΠ»ΠΈΡ‚Π΅Π»ΡŒΠ½Ρ‹ΠΉ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌ Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ‡ΠΈ Π½Π° основС Π°Π½Π°Π»ΠΎΠ³Π° ΠΊΠΎΠ½Π΅Ρ‡Π½ΠΎ-разностной схСмы ΠšΡ€Π°Π½ΠΊΠ° – Николсон с использованиСм Ρ„ΠΎΡ€ΠΌΡƒΠ»Ρ‹ Π“Ρ€ΡŽΠ½Π²Π°Π»ΡŒΠ΄Π° – Π›Π΅Ρ‚Π½ΠΈΠΊΠΎΠ²Π° для аппроксимации ΠΏΡ€ΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΠΎΠΉ Π΄Ρ€ΠΎΠ±Π½ΠΎΠ³ΠΎ порядка ΠΏΠΎ Π²Ρ€Π΅ΠΌΠ΅Π½ΠΈ. Аппроксимация Π³Ρ€Π°Π½ΠΈΡ‡Π½ΠΎΠ³ΠΎ условия НСймана учитываСтся Π² ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… уравнСниях ΠΏΡ€ΠΈ ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π΅ ΠΎΡ‚ Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΠ°Π»ΡŒΠ½ΠΎΠΉ Π·Π°Π΄Π°Ρ‡ΠΈ ΠΊ ΠΊΠΎΠ½Π΅Ρ‡Π½ΠΎ-разностной Π½Π° основС ввСдСния Ρ„ΠΈΠΊΡ‚ΠΈΠ²Π½Ρ‹Ρ… ΡƒΠ·Π»ΠΎΠ² сСтки. Π˜Ρ‚ΠΎΠ³ΠΎΠ²Π°Ρ систСма Π»ΠΈΠ½Π΅ΠΉΠ½Ρ‹Ρ… алгСбраичСских ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ Ρ€Π΅ΡˆΠ°Π΅Ρ‚ΡΡ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠΌ ΠΏΡ€ΠΎΠ³ΠΎΠ½ΠΊΠΈ.Π Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π° прикладная ΠΏΡ€ΠΎΠ³Ρ€Π°ΠΌΠΌΠ°, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‰Π°Ρ ΠΏΡ€ΠΎΠ²ΠΎΠ΄ΠΈΡ‚ΡŒ ΠΊΠΎΠΌΠΏΡŒΡŽΡ‚Π΅Ρ€Π½ΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ процСсса тСплопроводности для эрСдитарных срСд Π² ΠΎΠ΄Π½ΠΎΠΉ ΠΈΠ· частных постановок. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Π° ΠΏΡ€ΠΎΠ²Π΅Ρ€ΠΊΠ° адСкватности Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΎΠ² числСнного модСлирования Π½Π° тСст-Π·Π°Π΄Π°Ρ‡Π΅. Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΊΠΎΠΌΠΏΡŒΡŽΡ‚Π΅Ρ€Π½ΠΎΠ³ΠΎ модСлирования продСмонстрированы для ΠΏΡ€ΠΈΠΊΠ»Π°Π΄Π½ΠΎΠΉ Π·Π°Π΄Π°Ρ‡ΠΈ – ΠΎΡ†Π΅Π½ΠΊΠΈ Ρ‚Π΅ΠΌΠΏΠ΅Ρ€Π°Ρ‚ΡƒΡ€Π½ΠΎΠ³ΠΎ распрСдСлСния Π² ΠΎΠ±Ρ€Π°Π·Ρ†Π΅ Ρ‚ΠΈΠΏΠΈΡ‡Π½ΠΎΠ³ΠΎ сСгнСтоэлСктрика Ρ‚Ρ€ΠΈΠ³Π»ΠΈΡ†ΠΈΠ½ΡΡƒΠ»ΡŒΡ„Π°Ρ‚Π° ΠΏΡ€ΠΈ интСнсивном, ΠΏΠΎ ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΡŽ ΠΊ Ρ‚Π΅ΠΌΠΏΠ΅Ρ€Π°Ρ‚ΡƒΡ€Π΅ Ρ„Π°Π·ΠΎΠ²ΠΎΠ³ΠΎ ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π°, Ρ‚Π΅ΠΏΠ»ΠΎΠ²ΠΎΠΌ Π½Π°Π³Ρ€Π΅Π²Π΅. ΠŸΡ€ΠΈΠ±Π»ΠΈΠΆΠ΅Π½Π½ΠΎ ΠΎΡ†Π΅Π½Π΅Π½ порядок Π΄Ρ€ΠΎΠ±Π½ΠΎΠ³ΠΎ диффСрСнцирования (~0.7) Π½Π° основС сравнСния Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΎΠ² Ρ€Π΅Π°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ Ρ„Ρ€Π°ΠΊΡ‚Π°Π»ΡŒΠ½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ (ΠΏΡ€ΠΈ Π²Π°Ρ€ΡŒΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠΈ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Π°) с ΡΠΊΡΠΏΠ΅Ρ€ΠΈΠΌΠ΅Π½Ρ‚Π°Π»ΡŒΠ½Ρ‹ΠΌΠΈ Π΄Π°Π½Π½Ρ‹ΠΌΠΈ ΠΏΠΎ ΠΎΡ†Π΅Π½ΠΊΠ΅ Π²Ρ€Π΅ΠΌΠ΅Π½ΠΈ достиТСния Ρ‚Π΅ΠΌΠΏΠ΅Ρ€Π°Ρ‚ΡƒΡ€Ρ‹ ΠšΡŽΡ€ΠΈ. Π­Ρ‚ΠΎ ΡΠ²ΠΈΠ΄Π΅Ρ‚Π΅Π»ΡŒΡΡ‚Π²ΡƒΠ΅Ρ‚ ΠΎ нСобходимости использования ΠΌΠΎΠ΄ΠΈΡ„ΠΈΡ†ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΠΏΡ€ΠΈ Π°Π½Π°Π»ΠΈΠ·Π΅ ΠΏΠΎΠ»Π΅Π²Ρ‹Ρ… эффСктов, Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡŽΡ‰ΠΈΡ… Π² эрСдитарных срСдах

    Fractional-Differential Model of Heat Conductivity Process in Ferroelectrics under the Intensive Heating Conditions

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    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 – Nicolson finite difference scheme combining with the Grunwald – 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) / ΠžΠ‘ΠžΠ‘Π•ΠΠΠžΠ‘Π’Π˜ Π€Π£ΠΠšΠ¦Π˜ΠžΠΠ˜Π ΠžΠ’ΠΠΠ˜Π― ΠŸΠ›ΠžΠ©ΠΠ”ΠžΠš НА КРЫШАΠ₯ КАК ΠœΠ•Π‘Π’ Π‘ΠžΠ¦Π˜ΠΠ›Π¬ΠΠžΠ™ КОММУНИКАЦИИ (Π½Π° ΠΏΡ€ΠΈΠΌΠ΅Ρ€Π΅ кампуса Π’Π“Π£Π­Π‘ Π²ΠΎ ВладивостокС)

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    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. / ЦСль исслСдования состоит Π² раскрытии особСнностСй функционирования плоских эксплуатируСмых ΠΊΡ€Ρ‹Ρˆ Π² качСствС общСствСнных пространств Π½Π° ΠΏΡ€ΠΈΠΌΠ΅Ρ€Π΅ кампуса Π’Π“Π£Π­Π‘ Π² Π³ΠΎΡ€ΠΎΠ΄Π΅ ВладивостокС. \ud На этапС сбора исходных Π΄Π°Π½Π½Ρ‹Ρ… Π² исслСдовании ΠΏΡ€ΠΈΠΌΠ΅Π½ΡΠ»ΠΈΡΡŒ Ρ‚Π°ΠΊΠΈΠ΅ ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹, ΠΊΠ°ΠΊ наблюдСниС, фотографичСская фиксация ΠΈ социологичСский опрос Π² Ρ„ΠΎΡ€ΠΌΠ΅ анкСтирования. Π’ тСорСтичСской части исслСдования использовались ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹ аналитичСской Ρ„Π΅Π½ΠΎΠΌΠ΅Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π°Ρ€Ρ…ΠΈΡ‚Π΅ΠΊΡ‚ΡƒΡ€Ρ‹ ΠΈ структурно-сСмиотичСского Π°Π½Π°Π»ΠΈΠ·Π°. Π’ ΠΏΡ€ΠΎΠ΅ΠΊΡ‚Π½ΠΎ-ΡΠΊΡΠΏΠ΅Ρ€ΠΈΠΌΠ΅Π½Ρ‚Π°Π»ΡŒΠ½ΠΎΠΉ части исслСдования использовалось символичСскоС (рисунки, схСмы ΠΈ Ρ‡Π΅Ρ€Ρ‚Π΅ΠΆΠΈ) ΠΈ ΠΊΠΎΠΌΠΏΡŒΡŽΡ‚Π΅Ρ€Π½ΠΎΠ΅ (3D-сцСны) ΠΌΠΎΠ΄Π΅Π»ΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅.\ud Π’ ΡΡ‚Π°Ρ‚ΡŒΠ΅ Ρ€Π°ΡΡΠΌΠ°Ρ‚Ρ€ΠΈΠ²Π°ΡŽΡ‚ΡΡ Ρ€Π΅ΠΊΠ»Π°ΠΌΠ½ΠΎ-ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Π΅ ΠΈ Ρ€Π΅ΠΊΡ€Π΅Π°Ρ†ΠΈΠΎΠ½Π½Ρ‹Π΅ пространства, ΠΏΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Π΅ Π² Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Π΅ прСобразования повСрхностСй ΠΊΡ€ΠΎΠ²Π»ΠΈ, ΠΈ ΠΈΡ… ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡ‚ΡŒ Ρ€Π΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Ρ‚ΡŒ мноТСство ΡΠΎΡ†ΠΈΠ°Π»ΡŒΠ½ΠΎ-ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΉ. АнализируСтся Ρ€ΠΎΠ»ΡŒ Ρ‚Π°ΠΊΠΈΡ… пространств ΠΊΠ°ΠΊ ΠΊΠ°Ρ‚Π°Π»ΠΈΠ·Π°Ρ‚ΠΎΡ€ΠΎΠ² общСствСнной активности, символов соврСмСнности, Π·Π½Π°ΠΊΠΎΠ² Сдинства ΠΏΡ€ΠΈΡ€ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΈ Π°Ρ€Ρ…ΠΈΡ‚Π΅ΠΊΡ‚ΡƒΡ€Π½ΠΎΠ³ΠΎ окруТСния, индСксов высокого уровня комфортности срСды обитания, Π·Π°Π±ΠΎΡ‚Ρ‹ ΠΎ психологичСском Π·Π΄ΠΎΡ€ΠΎΠ²ΡŒΠ΅ общСства, ΠΏΠΎΠΊΠ°Π·Π°Ρ‚Π΅Π»Π΅ΠΉ статуса ΠΈ носитСлСй Ρ„ΠΈΡ€ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ стиля завСдСния, срСдств познания Π΄Π΅ΠΉΡΡ‚Π²ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ.\ud ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Π½ΠΎΠ΅ тСорСтичСскоС исслСдованиС ΠΈ практичСский экспСримСнт ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ ΡΠ΄Π΅Π»Π°Ρ‚ΡŒ Π²Ρ‹Π²ΠΎΠ΄ ΠΎΠ± эффСктивности ΠΈ пСрспСктивности использования повСрхностСй плоских ΠΊΡ€Ρ‹Ρˆ ΠΊΠ°ΠΊ мСст для ΡΠΎΡ†ΠΈΠ°Π»ΡŒΠ½ΠΎΠΉ ΠΊΠΎΠΌΠΌΡƒΠ½ΠΈΠΊΠ°Ρ†ΠΈΠΈ, способных ΠΎΠ±ΠΎΠ³Π°Ρ‚ΠΈΡ‚ΡŒ городской контСкст Π½ΠΎΠ²Ρ‹ΠΌΠΈ значСниями ΠΈ эстСтичСским содСрТаниСм, ΡΠΏΠΎΡΠΎΠ±ΡΡ‚Π²ΡƒΡŽΡ‰ΠΈΡ… ΠΏΠΎΠ²Ρ‹ΡˆΠ΅Π½ΠΈΡŽ общСствСнной активности ΠΈ ΡƒΠ²Π΅Π»ΠΈΡ‡Π΅Π½ΠΈΡŽ Ρ‚Π΅ΠΌ самым динамичСской плотности социума\ud \u
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