The 19 references with contexts in paper O. Pugachev V., Z. Han T., З. Хан Т., О. Пугачёв В. (2016) “Теплопроводность композита с нетеплопроводными шаровыми включениями // Heat Conductivity of Composite Materials with Included Balls of Zero Heat Conductivity” / spz:neicon:technomag:y:2015:i:5:p:205-217

1
Dul'nev G.N., Zarichniak Iu.P.Teploprovodnost' smesei i kompozitsionnykh materialov[Heat conductivity of mixtures and composite materials]. Leningrad, Energiia Publ., 1974. 264 p. (in Russian).
Total in-text references: 1
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    ÍÓÏÔÓÁËÚ‡Ï ÓÚÌÓÒËÚÒˇ ·ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı χÚÂˇÎÓ‚ ÔÓÒ‚ˇ ̆ÂÌ ̊ ÏÌÓ„Ë ‡·ÓÚ ̊ 60-80-ı „Ó‰Ó‚ ÔÓ ̄ÎÓ„Ó ‚Â͇
    Exact
    [1,2,3,4,5]
    Suffix
    . –‡Ò ̃ÂÚÌ ̊ ÙÓÏÛÎ ̊ ‚ ̋ÚËı ‡·ÓÚ‡ı ÔÓÎÛ ̃ÂÌ ̊, Í‡Í Ô‡‚ËÎÓ, ÎË·Ó ÔÛÚÂÏ Ó·‡·ÓÚÍË ̋ÍÒÔÂËÏÂÌڇΠ̧Ì ̊ı ‰‡ÌÌ ̊ı ÔËÏÂÌËÚÂÎ ̧ÌÓ Í ÍÓÌÍÂÚÌ ̊Ï Ï‡ÚÂˇ·Ï, ÎË·Ó ÔÛÚÂÏ ‡ÔËÓÌÓ„Ó Á‡‰‡Ìˡ ‡ÒÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ Ë ÚÂÔÎÓ‚Ó„Ó ÔÓÚÓ͇ ‚ ÏÓ‰ÂΡı ÒÚÛÍÚÛ ̊ „ÂÚÂÓ„ÂÌÌ ̊ı ÚÂÎ.

2
Missenard A.Conductivite thermique des solides, liquides, gaz et de leurs melanges. Paris, Editions Eyrolles, 1965. (In French). (Russ ed. Missenard A.Teploprovodnost' tverdykh tel, zhidkostey, gazov i ikh kompozitsiy. Moscow, Mir Publ., 1968. 464 p.).
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    Prefix
    ÍÓÏÔÓÁËÚ‡Ï ÓÚÌÓÒËÚÒˇ ·ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı χÚÂˇÎÓ‚ ÔÓÒ‚ˇ ̆ÂÌ ̊ ÏÌÓ„Ë ‡·ÓÚ ̊ 60-80-ı „Ó‰Ó‚ ÔÓ ̄ÎÓ„Ó ‚Â͇
    Exact
    [1,2,3,4,5]
    Suffix
    . –‡Ò ̃ÂÚÌ ̊ ÙÓÏÛÎ ̊ ‚ ̋ÚËı ‡·ÓÚ‡ı ÔÓÎÛ ̃ÂÌ ̊, Í‡Í Ô‡‚ËÎÓ, ÎË·Ó ÔÛÚÂÏ Ó·‡·ÓÚÍË ̋ÍÒÔÂËÏÂÌڇΠ̧Ì ̊ı ‰‡ÌÌ ̊ı ÔËÏÂÌËÚÂÎ ̧ÌÓ Í ÍÓÌÍÂÚÌ ̊Ï Ï‡ÚÂˇ·Ï, ÎË·Ó ÔÛÚÂÏ ‡ÔËÓÌÓ„Ó Á‡‰‡Ìˡ ‡ÒÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ Ë ÚÂÔÎÓ‚Ó„Ó ÔÓÚÓ͇ ‚ ÏÓ‰ÂΡı ÒÚÛÍÚÛ ̊ „ÂÚÂÓ„ÂÌÌ ̊ı ÚÂÎ.

3
Shermergor T.D.Teoriia uprugosti mikroneodnorodnykh sred[Theory of elasticity of microheterogeneous media]. Moscow, Nauka Publ., 1977. 400 p. (in Russian).
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    ÍÓÏÔÓÁËÚ‡Ï ÓÚÌÓÒËÚÒˇ ·ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı χÚÂˇÎÓ‚ ÔÓÒ‚ˇ ̆ÂÌ ̊ ÏÌÓ„Ë ‡·ÓÚ ̊ 60-80-ı „Ó‰Ó‚ ÔÓ ̄ÎÓ„Ó ‚Â͇
    Exact
    [1,2,3,4,5]
    Suffix
    . –‡Ò ̃ÂÚÌ ̊ ÙÓÏÛÎ ̊ ‚ ̋ÚËı ‡·ÓÚ‡ı ÔÓÎÛ ̃ÂÌ ̊, Í‡Í Ô‡‚ËÎÓ, ÎË·Ó ÔÛÚÂÏ Ó·‡·ÓÚÍË ̋ÍÒÔÂËÏÂÌڇΠ̧Ì ̊ı ‰‡ÌÌ ̊ı ÔËÏÂÌËÚÂÎ ̧ÌÓ Í ÍÓÌÍÂÚÌ ̊Ï Ï‡ÚÂˇ·Ï, ÎË·Ó ÔÛÚÂÏ ‡ÔËÓÌÓ„Ó Á‡‰‡Ìˡ ‡ÒÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ Ë ÚÂÔÎÓ‚Ó„Ó ÔÓÚÓ͇ ‚ ÏÓ‰ÂΡı ÒÚÛÍÚÛ ̊ „ÂÚÂÓ„ÂÌÌ ̊ı ÚÂÎ.

4
Zarubin V.S.Inzhenernye metody resheniia zadach teploprovodnosti[Engineering methods of solving problems of heat conductivity]. Moscow, Energoatomizdat Publ., 1983. 328 p. (in Russian).
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    ÍÓÏÔÓÁËÚ‡Ï ÓÚÌÓÒËÚÒˇ ·ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı χÚÂˇÎÓ‚ ÔÓÒ‚ˇ ̆ÂÌ ̊ ÏÌÓ„Ë ‡·ÓÚ ̊ 60-80-ı „Ó‰Ó‚ ÔÓ ̄ÎÓ„Ó ‚Â͇
    Exact
    [1,2,3,4,5]
    Suffix
    . –‡Ò ̃ÂÚÌ ̊ ÙÓÏÛÎ ̊ ‚ ̋ÚËı ‡·ÓÚ‡ı ÔÓÎÛ ̃ÂÌ ̊, Í‡Í Ô‡‚ËÎÓ, ÎË·Ó ÔÛÚÂÏ Ó·‡·ÓÚÍË ̋ÍÒÔÂËÏÂÌڇΠ̧Ì ̊ı ‰‡ÌÌ ̊ı ÔËÏÂÌËÚÂÎ ̧ÌÓ Í ÍÓÌÍÂÚÌ ̊Ï Ï‡ÚÂˇ·Ï, ÎË·Ó ÔÛÚÂÏ ‡ÔËÓÌÓ„Ó Á‡‰‡Ìˡ ‡ÒÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ Ë ÚÂÔÎÓ‚Ó„Ó ÔÓÚÓ͇ ‚ ÏÓ‰ÂΡı ÒÚÛÍÚÛ ̊ „ÂÚÂÓ„ÂÌÌ ̊ı ÚÂÎ.

5
Khoroshun L.P., Soltanov N.S.Termouprugost' dvukhkomponentnykh smesei[Thermoelasticity of two-component mixtures]. Kiev, Naukova dumka Publ., 1985. 109 p. (in Russian).
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    ÍÓÏÔÓÁËÚ‡Ï ÓÚÌÓÒËÚÒˇ ·ÓÎ ̧ ̄ËÌÒÚ‚Ó ÔËÏÂÌˇÂÏ ̊ı ‚ ÚÂıÌËÍ χÚÂˇÎÓ‚, ˇ‚Ρ ̨ ̆ËıÒˇ „ÂÚÂÓ„ÂÌÌ ̊ÏË Ú‚Â‰ ̊ÏË Ú·ÏË. »ÒÒΉӂ‡ÌË ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ú‡ÍËı χÚÂˇÎÓ‚ ÔÓÒ‚ˇ ̆ÂÌ ̊ ÏÌÓ„Ë ‡·ÓÚ ̊ 60-80-ı „Ó‰Ó‚ ÔÓ ̄ÎÓ„Ó ‚Â͇
    Exact
    [1,2,3,4,5]
    Suffix
    . –‡Ò ̃ÂÚÌ ̊ ÙÓÏÛÎ ̊ ‚ ̋ÚËı ‡·ÓÚ‡ı ÔÓÎÛ ̃ÂÌ ̊, Í‡Í Ô‡‚ËÎÓ, ÎË·Ó ÔÛÚÂÏ Ó·‡·ÓÚÍË ̋ÍÒÔÂËÏÂÌڇΠ̧Ì ̊ı ‰‡ÌÌ ̊ı ÔËÏÂÌËÚÂÎ ̧ÌÓ Í ÍÓÌÍÂÚÌ ̊Ï Ï‡ÚÂˇ·Ï, ÎË·Ó ÔÛÚÂÏ ‡ÔËÓÌÓ„Ó Á‡‰‡Ìˡ ‡ÒÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ Ë ÚÂÔÎÓ‚Ó„Ó ÔÓÚÓ͇ ‚ ÏÓ‰ÂΡı ÒÚÛÍÚÛ ̊ „ÂÚÂÓ„ÂÌÌ ̊ı ÚÂÎ.

6
Kats E.A.Fullereny, uglerodnye nanotrubki i nanoklastery. Rodoslovnaya form i idey [Fullerens, carbon nano-tubes and nano-clusters. The family-tree of form and ideas]. Moscow, LKI Publ., 2008. 296 p. (in Russian).
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    ≈ÒÎË ‚ÍÎ ̨ ̃ÂÌˡ ‚ ÍÓÏÔÓÁËÚ ËÏ ̨Ú ·ÎËÁÍË ‡ÁÏÂ ̊ ‚Ó ‚ÒÂı ̇Ô‡‚ÎÂÌˡı, ÚÓ ‚ ÔÂ‚ÓÏ ÔË·ÎËÊÂÌËË Ëı ÏÓÊÌÓ ‡ÒÒχÚË‚‡Ú ̧ Í‡Í ̄‡Ó‚ ̊Â. ‘ÓÏÛ, ·ÎËÁÍÛ ̨ Í ̄‡Û, ËÏ ̨Ú Ë ÌÂÍÓÚÓ ̊ ̇ÌÓÒÚÛÍÚÛÌ ̊ ̋ÎÂÏÂÌÚ ̊ (‚ ÚÓÏ ̃ËÒΠÙÛÎÎÂÂÌ ̊), ÍÓÚÓ ̊ ‚ ÔÓÒΉÌ ‚ÂÏˇ ÔËÏÂÌˇ ̨ÚÒˇ Í‡Í ‚ÍÎ ̨ ̃ÂÌˡ ‰Îˇ ÍÓÏÔÓÁËÚÓ‚ ‡ÁÎË ̃ÌÓ„Ó Ì‡Á̇ ̃ÂÌˡ
    Exact
    [6]
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    . ƒÎˇ ÍÓÏÔÓÁËÚ‡ Ò ̄‡Ó‚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË Û‰‡ÂÚÒˇ ÔÓÒÚÓËÚ ̧ ‡‰ÂÍ‚‡ÚÌ ̊ χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ‰ÓÒÚ‡ÚÓ ̃ÌÓ ‰ÓÒÚÓ‚ÂÌÓ ÔÓ„ÌÓÁËÛ ̨ ̆Ë Á‡‚ËÒËÏÓÒÚ ̧ Â„Ó ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÓÚ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡Úˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ë ÓÚ Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËË ‚ÍÎ ̨ ̃ÂÌËÈ.

7
Golovin N.N., Zarubin V.S., Kuvyrkin G.N. Estimation of effective heat conductivity coefficient of fullerene-modified composite material.Kompozity i nanostruktury=Composites and Nanostructures, 2012, no. 4, pp. 15{22. (in Russian).
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    ÂÌ ̊), ÍÓÚÓ ̊ ‚ ÔÓÒΉÌ ‚ÂÏˇ ÔËÏÂÌˇ ̨ÚÒˇ Í‡Í ‚ÍÎ ̨ ̃ÂÌˡ ‰Îˇ ÍÓÏÔÓÁËÚÓ‚ ‡ÁÎË ̃ÌÓ„Ó Ì‡Á̇ ̃ÂÌˡ [6]. ƒÎˇ ÍÓÏÔÓÁËÚ‡ Ò ̄‡Ó‚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË Û‰‡ÂÚÒˇ ÔÓÒÚÓËÚ ̧ ‡‰ÂÍ‚‡ÚÌ ̊ χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ‰ÓÒÚ‡ÚÓ ̃ÌÓ ‰ÓÒÚÓ‚ÂÌÓ ÔÓ„ÌÓÁËÛ ̨ ̆Ë Á‡‚ËÒËÏÓÒÚ ̧ Â„Ó ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÓÚ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡Úˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ë ÓÚ Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËË ‚ÍÎ ̨ ̃ÂÌËÈ. ¬ ‡·ÓÚ‡ı
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    [7,8,9]
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

8
Zarubin V.S.,Kuvyrkin G.N.,Savel'eva I.Iu.The Effective Coefficients of Thermal Conductivity of Composites with Spherical Inclusions.Teplovye protsessy v tekhnike=Thermal Processes in Engineering, 2012, no. 10, pp. 470{474. (in Russian).
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    ÂÌ ̊), ÍÓÚÓ ̊ ‚ ÔÓÒΉÌ ‚ÂÏˇ ÔËÏÂÌˇ ̨ÚÒˇ Í‡Í ‚ÍÎ ̨ ̃ÂÌˡ ‰Îˇ ÍÓÏÔÓÁËÚÓ‚ ‡ÁÎË ̃ÌÓ„Ó Ì‡Á̇ ̃ÂÌˡ [6]. ƒÎˇ ÍÓÏÔÓÁËÚ‡ Ò ̄‡Ó‚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË Û‰‡ÂÚÒˇ ÔÓÒÚÓËÚ ̧ ‡‰ÂÍ‚‡ÚÌ ̊ χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ‰ÓÒÚ‡ÚÓ ̃ÌÓ ‰ÓÒÚÓ‚ÂÌÓ ÔÓ„ÌÓÁËÛ ̨ ̆Ë Á‡‚ËÒËÏÓÒÚ ̧ Â„Ó ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÓÚ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡Úˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ë ÓÚ Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËË ‚ÍÎ ̨ ̃ÂÌËÈ. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

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    “ ‡ · Î Ë ˆ ‡ 2 rPˆa/aˆλ/λ 0,20,603...0,6320,94...1,000,91...0,97 0,30,583...0,6120,90...0,960,80...0,86 0,40,564...0,5940,87...0,930,64...0,68 0,50,519...0,5490,79...0,840,38...0,40 —‡‚ÌËÏ ÔÓÎÛ ̃ÂÌÌ ̊ ̇ÏË ÂÁÛÎ ̧Ú‡Ú ̊ Ò ÂÁÛÎ ̧Ú‡Ú‡ÏË ‡·ÓÚ ̊
    Exact
    [8]
    Suffix
    . —ӄ·ÒÌÓ ÙÓÏÛÎÂ λˆ λ = 1− 3α 2 +α ,(7) „‰Âα| Ó· ̇ÂÏ̇ˇ ÍÓ̈ÂÌÚ‡ˆËˇ ÚÂÔÎÓËÁÓÎËÛ ̨ ̆Ëı ‚ÍÎ ̨ ̃ÂÌËÈ. ¬ ‰‡ÌÌÓÈ ÒËÚÛ‡ˆËËα= 4πr3/3. ¬ Ú‡·Î.3ÒÓÔÓÒÚ‡‚ÎÂÌ ̊ ‚ÂÎË ̃ËÌ ̊ˆλ/λËÁ Ú‡·Î.1,2Ë ÔÓ ÙÓÏÛΠ(7). “ ‡ · Î Ë ˆ ‡ 3 r“‡·Î. 1“‡·Î. 2(7) 0,20,91...0,970,91...0,970,95 0,30,84...0,900,80...0,860,84 0,40,61...0,640,64...0,680,65 0,50,32...0,350,38...0,400,38 ¬ ÒÎÛ ̃‡Â ı‡ÓÚË ̃ÂÒÍÓ„Ó ‡ÒÔÓÎÓÊÂÌˡ ‚ÍÎ ̨ ̃ÂÌËÈ

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    “ ‡ · Î Ë ˆ ‡ 3 r“‡·Î. 1“‡·Î. 2(7) 0,20,91...0,970,91...0,970,95 0,30,84...0,900,80...0,860,84 0,40,61...0,640,64...0,680,65 0,50,32...0,350,38...0,400,38 ¬ ÒÎÛ ̃‡Â ı‡ÓÚË ̃ÂÒÍÓ„Ó ‡ÒÔÓÎÓÊÂÌˡ ‚ÍÎ ̨ ̃ÂÌËÈ ÂÁÛÎ ̧Ú‡Ú ̊ ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ̋ÍÒÔÂËÏÂÌÚÓ‚ Òӄ·ÒÛ ̨ÚÒˇ Ò ÔÓÎÛ ̃ÂÌÌ ̊ÏË ‡Ì‡ÎËÚË ̃ÂÒÍË
    Exact
    [8]
    Suffix
    . ÕÂÚÛ‰ÌÓ Á‡ÏÂÚËÚ ̧, ̃ÚÓ ‚ ÒÎÛ ̃‡Â ÛÔÓˇ‰Ó ̃ÂÌÌ ̊ı ‚ÍÎ ̨ ̃ÂÌËÈ ·ÓÎ ̧ ̄Ëı ‡ÁÏÂÓ‚ ̋ÙÙÂÍÚ˂̇ˇ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧ ÔÓÎÛ ̃‡ÂÚÒˇ ÏÂÌ ̧ ̄Â, ̋ÚÓ Ó· ̇ˇÒÌˇÂÚÒˇ ÛÁÍËÏË ÔÓıÓ‰‡ÏË ÏÂÊ‰Û ÚÂÔÎÓËÁÓÎËÛ ̨ ̆ËÏË ̄‡Ë͇ÏË, ÎÂʇ ̆ËÏË ÛÔÓˇ‰Ó ̃ÂÌÌ ̊Ï ÒÎÓÂÏ.

9
Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. Thermal Conductivity of Composite Reinforced with Fibers.Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie=Proceedings of Higher Educational Institutions. Machine Building, 2013, no. 5, pp. 75{81. (in Russian).
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    ÂÌ ̊), ÍÓÚÓ ̊ ‚ ÔÓÒΉÌ ‚ÂÏˇ ÔËÏÂÌˇ ̨ÚÒˇ Í‡Í ‚ÍÎ ̨ ̃ÂÌˡ ‰Îˇ ÍÓÏÔÓÁËÚÓ‚ ‡ÁÎË ̃ÌÓ„Ó Ì‡Á̇ ̃ÂÌˡ [6]. ƒÎˇ ÍÓÏÔÓÁËÚ‡ Ò ̄‡Ó‚ ̊ÏË ‚ÍÎ ̨ ̃ÂÌˡÏË Û‰‡ÂÚÒˇ ÔÓÒÚÓËÚ ̧ ‡‰ÂÍ‚‡ÚÌ ̊ χÚÂχÚË ̃ÂÒÍË ÏÓ‰ÂÎË, ‰ÓÒÚ‡ÚÓ ̃ÌÓ ‰ÓÒÚÓ‚ÂÌÓ ÔÓ„ÌÓÁËÛ ̨ ̆Ë Á‡‚ËÒËÏÓÒÚ ̧ Â„Ó ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÓÚ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡Úˈ ̊ Ë ‚ÍÎ ̨ ̃ÂÌËÈ Ë ÓÚ Ó· ̇ÂÏÌÓÈ ÍÓ̈ÂÌÚ‡ˆËË ‚ÍÎ ̨ ̃ÂÌËÈ. ¬ ‡·ÓÚ‡ı
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    · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ.

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Zarubin V.S., Kotovich A.V., Kuvyrkin G.N. Estimates of the effective coefficient of heat conductivity of a composite with anisotropic ball inclusions.Izvestiya RAN. Energetika= Proceedings of RAS. Energetics, 2012, no. 6, pp. 118{126. (in Russian).
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    ¬ ‡·ÓÚ‡ı [7,8,9] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
    Exact
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Zarubin V.S., Kuvyrkin G.N. Effective Coefficients of Thermal Conductivity of a Composite with Ellipsoidal Inclusions.Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki= Herald of the Bauman Moscow State Technical University. Ser. Natural sciences, 2012, no. 3, pp. 76{85. (in Russian).
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    ¬ ‡·ÓÚ‡ı [7,8,9] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. Comparative analysis of estimations of heat conduction of a composite with ball inclusions.Nauka i obrazovanie MGTU im. N.E. Baumana=Science and Education of the Bauman MSTU, 2013, no. 7, pp. 299{318. DOI: 10.7463/0713.0569319(in Russian).
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    ¬ ‡·ÓÚ‡ı [7,8,9] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
    Exact
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Zarubin V.S., Kuvyrkin G.N., Savel'eva I.Iu. Evaluation of effective thermal conductivity of composites with ball inclusions by the method of self-consistency.Nauka i obrazovanie MGTU im. N.E. Baumana=Science and Education of the Bauman MSTU, 2013, no. 9, pp. 435{444. DOI:10.7463/0913.0601512(in Russian).
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    ¬ ‡·ÓÚ‡ı [7,8,9] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
    Exact
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Yankovskii A.P. Numerically-Analytical Modelling of Processes of Thermal Conductivity in Spatially Reinforced Composites at Intensive Thermal Action.Teplovye protsessy v tekhnike =Thermal Processes in Engineering, 2011, no. 11, pp. 500{516. (in Russian).
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    ¬ ‡·ÓÚ‡ı [7,8,9] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
    Exact
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Chen Y.-M., Ting J.-M. Ultra high thermal conductivity polymer composites.Carbon, 2002, vol. 40, no. 3, pp. 359{362. DOI:10.1016/S0008-6223(01)00112-9
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    ¬ ‡·ÓÚ‡ı [7,8,9] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
    Exact
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

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Nan C.-W., Birringer R., Clarke D.R., Gleiter H. Effective thermal conductivity of particulate composites with interfacial thermal resistance.Journal of Applied Physics, 1997, vol. 81, no. 10, pp. 6692{6699. DOI:10.1063/1.365209
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    ¬ ‡·ÓÚ‡ı [7,8,9] · ̊ÎË ÔËÏÂÌÂÌ ̊ ÌÓ‚ ̊ ÔÓ‰ıÓ‰ ̊ Í Á‡‰‡ ̃ ӈÂÌÍË ̋ÙÙÂÍÚË‚ÌÓ„Ó ÍÓ ̋ÙÙˈËÂÌÚ‡ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË Ï‡ÚÂˇ· Ò ‚ÍÎ ̨ ̃ÂÌˡÏË ÓÔ‰ÂÎÂÌÌÓÈ ÙÓÏ ̊ ËÁ ‰Û„Ó„Ó Ï‡ÚÂˇ·. »ÒÔÓÎ ̧ÁÓ‚‡ÎËÒ ̧ ÏÂÚÓ‰ ̊ ‚‡ˇˆËÓÌÌÓ„Ó ËÒ ̃ËÒÎÂÌˡ, ÔË ̋ÚÓÏ ‡ÒÒχÚË‚‡Î‡Ò ̧ ÛÔÓ ̆ÂÌ̇ˇ ÏÓ‰ÂÎ ̧ ÓÍÂÒÚÌÓÒÚË ‚ÍÎ ̨ ̃ÂÌˡ. »Á ÒÓ‚ÂÏÂÌÌ ̊ı ‡·ÓÚ ÔÓ ̋ÚÓÈ ÚÂÏ ÓÚÏÂÚËÏ Ú‡ÍÊÂ
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    [10,11,12,13,14,15,16]
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    . ¬ÓÁÓÒ ̄‡ˇ ÏÓ ̆ÌÓÒÚ ̧ ÒÓ‚ÂÏÂÌÌ ̊ı ÍÓÏÔ ̧ ̨ÚÂÓ‚ ÔÓÁ‚ÓΡÂÚ ÔËÏÂÌËÚ ̧ ÔË̈ËÔˇΠ̧ÌÓ ‰Û„ÓÈ ÔÓ‰ıÓ‰ Í  ̄ÂÌË ̨ Á‡‰‡ ̃Ë Ó· ̋ÙÙÂÍÚË‚ÌÓÈ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË. œÓˆÂÒÒ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ÏÓÊÌÓ ÏÓ‰ÂÎËÓ‚‡Ú ̧ ÔË ÔÓÏÓ ̆Ë ‰ËÙÙÛÁËÓÌÌ ̊ı ÔÓˆÂÒÒÓ‚, Ú.

17
Tikhonov A.N., Samarskii A.A.Uravneniia matematicheskoi fiziki[Equations of mathematical physics]. Moscow, MSU Publ., 1999. 799 p. (in Russian).
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  1. In-text reference with the coordinate start=4689
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    ÓÔÌ ̊Ï Ï‡ÚÂˇÎÓÏ Ò Ó· ̇ÂÏÌÓÈ ÚÂÔÎÓÂÏÍÓÒÚ ̧ ̨C (ƒÊ/Ï3K) Ë ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚËλ(¬Ú/Ï ), ÚÓ„‰‡ Û‡‚ÌÂÌË ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË ËÏÂÂÚ ‚ˉ u ̇=a∇2u,(1) „‰Âu=u(t,x,y,z)| ÚÂÏÔÂ‡ÚÛ‡ (ÓÚÒ ̃ËÚ ̊‚‡Âχˇ ÓÚ ÌÂÍÓÚÓÓ„Ó ‚ ̊·‡ÌÌÓ„Ó ÌÛΡ, Ì ӷˇÁ‡ÚÂÎ ̧ÌÓ ‡·ÒÓÎ ̨ÚÌÓ„Ó);a=λ/C(Ï2/c) | ÍÓ ̋ÙÙˈËÂÌÚ ÚÂÏÔÂ‡ÚÛÓÔÓ‚Ó‰ÌÓÒÚË. ≈ÒÎË ËÁ‚ÂÒÚÌÓ Ì‡ ̃‡Î ̧ÌÓ ‡ÒÔ‰ÂÎÂÌË ÚÂÏÔÂ‡ÚÛ ̊u0(x,y,z), ÚÓ ÏÓÊÌÓ ÔÓÎÛ ̃ËÚ ̧
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    [17]
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    ‡ÒÔ‰ÂÎÂÌË ÚÂÏÔÂ‡ÚÛ ̊ ̃ÂÂÁ ‚ÂÏˇtÔË ÔÓÏÓ ̆Ë Ò‚ÂÚÍË u(t,x,y,z) =u0∗pt(x,y,z),(2) „‰Â ÙÛÌÍˆËˇ pt(x,y,z) = 1 (√ 4πat )3exp ( − x2+y2+z2 4at ) (3) ÂÒÚ ̧ ÔÎÓÚÌÓÒÚ ̧ ÌÓχΠ̧ÌÓ„Ó ‡ÒÔ‰ÂÎÂÌˡ Ò ÌÛ΂ ̊Ï Ò‰ÌËÏ, ‰ËÒÔÂÒˡÏËDx= =Dy= Dz= 2atË ÌÛ΂ ̊ÏË ÍÓÂΡˆËˇÏË.

18
Venttsel' A.D.Kurs teorii sluchainykh protsessov[Course of the theory of random processes]. Moscow, Nauka Publ., 1975. 320 p. (in Russian).
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  1. In-text reference with the coordinate start=5066
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    ÂÎÂÌË ÚÂÏÔÂ‡ÚÛ ̊u0(x,y,z), ÚÓ ÏÓÊÌÓ ÔÓÎÛ ̃ËÚ ̧ [17] ‡ÒÔ‰ÂÎÂÌË ÚÂÏÔÂ‡ÚÛ ̊ ̃ÂÂÁ ‚ÂÏˇtÔË ÔÓÏÓ ̆Ë Ò‚ÂÚÍË u(t,x,y,z) =u0∗pt(x,y,z),(2) „‰Â ÙÛÌÍˆËˇ pt(x,y,z) = 1 (√ 4πat )3exp ( − x2+y2+z2 4at ) (3) ÂÒÚ ̧ ÔÎÓÚÌÓÒÚ ̧ ÌÓχΠ̧ÌÓ„Ó ‡ÒÔ‰ÂÎÂÌˡ Ò ÌÛ΂ ̊Ï Ò‰ÌËÏ, ‰ËÒÔÂÒˡÏËDx= =Dy= Dz= 2atË ÌÛ΂ ̊ÏË ÍÓÂΡˆËˇÏË. Œ‰ÌÓÏÂÌ ̊È ÒÎÛ ̃‡ÈÌ ̊È ÔÓˆÂÒÒ{wτ}τ>0̇Á ̊‚‡ÂÚÒˇ Òڇ̉‡ÚÌ ̊Ï ‚ËÌÂÓ‚ÒÍËÏ
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    , ÂÒÎËwτ∼N(0,τ), Ë Â„Ó ÔË‡ ̆ÂÌˡ wτ2−wτ1,...,wτk−wτk−1,06τ1<τ2<...<τk ÌÂÁ‡‚ËÒËÏ ̊. œ‡‡ÏÂÚτËÏÂÂÚ ‡ÁÏÂÌÓÒÚ ̧ Í‚‡‰‡Ú‡ ‡ÒÒÚÓˇÌˡ. ≈ÒÎË ÍÓÏÔÓÌÂÌÚ ̊ξt,ηt,ζtÚÂıÏÂÌÓ„Ó ÒÎÛ ̃‡ÈÌÓ„Ó ÔÓˆÂÒÒ‡ | ÌÂÁ‡‚ËÒËÏ ̊ ‚ËÌÂÓ‚ÒÍË ÔÓˆÂÒÒ ̊ Ò ‡ÒÔ‰ÂÎÂÌËÂÏN(0,2at), ÚÓ ÔÎÓÚÌÓÒÚ ̧ ‡ÒÔ‰ÂÎÂÌˡ ÒÎÛ ̃‡ÈÌÓÈ ‚ÂÎË ̃ËÌ ̊(ξt,ηt,ζt)ÔË Á‡‰‡ÌÌÓÏt>0‚ ̊‡Ê‡ÂÚÒˇ ÙÓÏÛÎÓÈ (3).

  2. In-text reference with the coordinate start=8109
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    –‡ÒÒ ̃ËÚ‡ÂÏ ̋ÚÛ ‚ÂÓˇÚÌÓÒÚ ̧ ‰Îˇ Ó‰ÌÓÓ‰ÌÓ„Ó Ï‡ÚÂˇ· Ò ÍÓ ̋ÙÙˈËÂÌÚÓÏ ÚÂÏÔÂ‡ÚÛÓÔÓ‚Ó‰ÌÓÒÚËa. œÛÒÚ ̧{wt}t>0| Òڇ̉‡ÚÌ ̊È ‚ËÌÂÓ‚ÒÍËÈ ÔÓˆÂÒÒ. ¡Û‰ÂÏ Ó·ÓÁ̇ ̃‡Ú ̧ ÒËÏ‚ÓÎÓÏτb ÔÂ‚ ̊È ÏÓÏÂÌÚ ‰ÓÒÚËÊÂÌˡ Á̇ ̃ÂÌˡb6= 0, Ú.Â. τb= min{t>0:wt=b}. —ӄ·ÒÌÓ ÔË̈ËÔÛ ÓÚ‡ÊÂÌˡ
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    , ÔÓˆÂÒÒ{Rbwt}, ÔÓÎÛ ̃ÂÌÌ ̊È ÓÚ‡ÊÂÌËÂÏ{wt}ÓÚ ÚÓ ̃ÍË bÔË ÔÂ‚ÓÏ ÔÓÔ‡‰‡ÌËË ‚ ÌÂÂ, Ú.Â. Rbwt=    wt,t∈[0,τb]; 2b−wt,t∈(τb,∞), Ú‡ÍÊ ·Û‰ÂÚ Òڇ̉‡ÚÌ ̊Ï ‚ËÌÂÓ‚ÒÍËÏ. œÓÎ ̧ÁÛˇÒ ̧ ̋ÚËÏ Ò‚ÓÈÒÚ‚ÓÏ ‚ËÌÂÓ‚ÒÍËı ÔÓˆÂÒÒÓ‚, ̇ȉÂÏ ‡ÒÔ‰ÂÎÂÌË ÒÎÛ ̃‡ÈÌÓ„Ó ÏÓÏÂÌÚ‡ Tb= min{t>0:|wt|=b},b>0.

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Pechinkin A.V., Teskin O.I., Tsvetkova G.M., Bocharov P.P., Kozlov N.E.Teoriia veroiatnostei[Probability theory]. Moscow, Bauman MSTU Publ., 2004. 456 p. (Ser.Matematika v tekhnicheskom universitete[Mathematics in Technical University], vol. 16). (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=10107
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    ‘ËÁË ̃ÂÒÍËÈ ÒÏ ̊ÒÎ Ú‡ÍÓ„Ó ̋ÍÒÔÂËÏÂÌÚ‡ | ÔËÎÓÊË‚ Í ÔÓ‚ÂıÌÓÒÚË{x= 0}‡‚ÌÓÏÂÌ ̊È ËÒÚÓ ̃ÌËÍ ÚÂÔ·, ÓˆÂÌËÚ ̧, ̇ÒÍÓÎ ̧ÍÓ · ̊ÒÚÓ ÓÌÓ ‰ÓıÓ‰ËÚ ‰Ó ÔÓ‚ÂıÌÓÒÚË{x=b}. Œ·ÓÁ̇ ̃ËÏq=m/n. —ӄ·ÒÌÓ ˆÂÌÚ‡Î ̧ÌÓÈ Ô‰ÂÎ ̧ÌÓÈ ÚÂÓÂÏÂ
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    95%-‰Ó‚ÂËÚÂÎ ̧Ì ̊È ËÌÚÂ‚‡Î ‰ÎˇPËÏÂÂÚ ‚ˉ P1=q−1,96 √ q(1−q) n <P<q+ 1,96 √ q(1−q) n =P2, ÒΉӂ‡ÚÂÎ ̧ÌÓ, 95%-‰Ó‚ÂËÚÂÎ ̧Ì ̊È ËÌÚÂ‚‡Î ‰ÎˇˆaËÏÂÂÚ ‚ˉ b2 2T F−11(P1)<ˆa< b2 2T F−11(P2). ›ÙÙÂÍÚË‚ÌÛ ̨ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚ ̧ ̇ȉÂÏ, ÛÏÌÓÊË‚ ̋ÙÙÂÍÚË‚ÌÛ ̨ ÚÂÏÔÂ‡ÚÛÓÔÓ‚Ó‰ÌÓÒÚ ̧ ̇ ÒÂ‰Ì ̨ ̨ Ó· ̇ÂÏÌÛ ̨ ÚÂÔÎÓÂÏÍÓÒÚ ̧: λˆ= ˆa ( C1(1−α) +C2α ) ,(6) „‰Âα| ‰ÓΡ Ó· ̇Âχ ÍÓÏÔÓÁËÚ‡, Á‡ÌËχÂχˇ ‚ÍÎ ̨ ̃ÂÌˡÏË.