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1. ;_kdbg<K?ebk__\ZK:I:@lk 2. Azoumanian Z., Chernoff D. F., Cordes (2003), ApJ, v568, p289; 3. Hobbs G., et al. (2005), MNRAS, v360, p963; 4. Kaspi V. M. (1998), AdSpR, v21, p176.

M>D

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EHFHGHKH<– 2006

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E–mail: [email protected]

1. Apanasenko A. V., et al., Composition and energy spectra of cosmic ray primaries in

the energy range 1013-1015 eV/particle observed by Japanese-Russian joint balloon experiment. //Astropart. Physics. 16(2001). p.13-46

2. GZaZjh\CGFh^_ebjh\Zgb_ ijhp_kkZ j_]bkljZpbb dhkfbq_kdh]hbaemq_gby\ukhdbowg_j]bc^eyh[jZ[hldb^Zgguowfmevkbhgguobq_j_gdh\kdbowdki_jbf_glh\ >bkk_jlZpby gZ khbkdZgb_ mq_ghc kl_i_gb dZg^b^ZlZ nbabdh-fZl_fZlbq_kdbogZmd

3. =Zedbg_j[bgZ<:AZfqZeh\Z?:b^jBa\J:Gk_jnbabqL1k-1592.

4. CERN/ASD Group. GEANT Detector Description and Simulation Tool, CERN Pro-gram Library W5013. CERN, 1994. T. Fujinaga, M. Ichimura, Y. Niihori and T. Shi-bata, Nucl. Instr. and Methods, A276 (1989) p.317-339.

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– qtZee →→−+ ** ,γ [4]; HERA – tXepe ±± → [5]; < ^Zgghc jZ[hl_ [ueh bkke_^h\Zgh h^bghqgh_ jh`^_gb_ t-d\Zjdh\ aZ kq_l

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EHFHGHKH<– 2006

18

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%13)( ,Lw< 4,0 1- <→<Λ gqtBRtgqκ .

1. Glashow S.L., Iliopoulos J. and Maiani L., Phys. Rev. Lett. D2, 1285 (1970). 2. Atwood D., Reina L. and Soni A., Phys. Rev., D55, 3156 (1997) [arXiv:hep-

ph/9609279]; Yang J.M., Young B.-L. and Zhang X., Phys. Rev., D58, 055001 (1998) [arXiv:hep-ph/9705341].

3. Abe F. et al. [CDF Collaboration], Phys. Rev. Lett. 80, 2525 (1998). 4. Abdallah J. et al. [DELPHI Collaboration], Preprint CERN-EP/2003-066, 2004

[arXiv:hep-ex/0404014] (and references therein). 5. Wolf G., [arXiv:hep-ex/0105055]; Alan A.T. and Senol A., Europhys. Lett. 57, 669

(2002) [arXiv:hep-ph/0202119]; Dannheim H. [H1 Collaboration], [arXiv:hep-ex/0212004].

6. Aktas A. et al. [H1 Collaboration], Eur. Phys. C33, 9 (2004) [arXiv:hep-ex/0310032]; Chekanov S. et al. [ZEUS Collaboration], Phys. Lett. B559, 153 (2003) [arXiv:hep-ex/0302010].

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20

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1. T.Murakami et al., Phys. Rev C, 34 (1986) 1353.

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Ij_êZ]Z_fucf_lh^khklhblba • jZkq_lZ [Zau ^Zgguo êy q_j_gdh\kdh]h k\_lZ ijb wg_j]byo gb`_ =w< êy

we_dljhgh\bnhlhgh\ • jZkq_lZnmgdpbbbklhqgbdZêywe_dljhgh\bnhlhgh\gb`_ihjh]h\hcwg_j]bb

hli_j\bqghcqZklbpumevljZ\ukhdhcwg_j]bb • \hkklZgh\e_gbyNIJQK=:EihnmgdpbyfbklhqgbdZbjZkkqblZgghc;> • hp_gdbwg_j]bb=:E

:\lhj\ujZ`Z_lijbagZl_evghklv^nfgJh]Zgh\hcbijhn_kkhjm^nfg>_^_gdhE=aZihfhsv\ih^]hlh\d_l_abkh\


1. Auger collaboration, Nuclear Instruments and Methods in Physics Research A 523 (2004) 50–95

2. D. Heck and J. Knapp, Report FZKA 6097, Forschungszentrum Karlsruhe, (1998). 3. L.G. Dedenko et. al. A Calibration of Energy Estimates of Giant Air Showers with

Help of the Cherenkov Radiation, 29th ICRC, Pune, India

BAMQ?GB?J:KI:>H<Kl3 (K±:π0 l± νl)

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EHFHGHKH<– 2006

22

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EHFHGHKH<– 2006

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1. R. D. DuBois, A. C. F. Santos, Th. Stohlker et al. // Phys. Rev. A., Vol. 70, P. 032712, 2004.

2. FZl\__\<BFZljZkmeh\>MJy[q_gdhK<IbkvfZ\@WLNLN 7, K-459, 2005.

3. FZl\__\<BFZljZkmeh\>MJy[q_gdhK<@WLNLNK-13, 2006.

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EHFHGHKH<– 2006

26

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JZ[hlZ\uiheg_gZijbnbgZgkh\hcih^^_j`d_]jZglh\JNNBrbnj]jZglZ-02-16177-ZbIj_ab^_glZJNrbnj]jZglZFD-2013.2005.2).


1. FZl\__\ <BJZobfh\ OX@WLN114, 1646-1661 (1998). 2. FZl\__\<B=mkZj_\bq?K@WLN123, 42-48 (2003).

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27

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28

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EHFHGHKH<– 2006

30

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1. Dh\Ze_gdhB;HWDO;bhnbabdZ-665 (2003) 2. <_jrm[kdbc:<Ijbdehgkdbc<BLbohgh\:G ;bhnbabdZ

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32

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Ih^k_dpby[bhnbabdb

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<ukrZyrdheZk 3. Inoue Y. Photosynthetic thermoluminescence as a simple probe of photosystem II

electron transport. In Biophysical Techqniques in photosynthesis, eds. by Amesz J., Hoff A.J., Kluwer Academic Publishers, 1996, pp 93-107.

M>D 577.3

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34

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1. DhfbkkZjh\ == ³Nhlhkbgl_a nbabdh-obfbq_kdbc ihôh^´ Obfbq_kdZy

nbabdZl k 24-54. 2. Karavaev V.A., Polyakova I.B., Solntsev M.K., Yurina T.P. Effect of various chemi-

cal agents on photosynthesis studied by the method of fluorescence induction // Jour-nal of Luminescence, 1998. V.76. P. 335-338.

3. DZjZ\Z_\ <: Iheydh\Z B; <ebygb_ 1D2HPO4 gZ f_ê_ggmx bg^mdpbx

nemhj_kp_gpbbbnhlhkbgl_aebklv_\[h[h\Nbabheh]byjZkl_gbcL 45. K 5-10.

4. Karavaev V.A., Dovydkov S.A., Polyakova I.B., Solntsev M.K., Yurina T.P. Slow fluorescence induction and O2 evolution in bean and wheat leaves in various physio-logical conditions // In: Photosynthesis: Mechanisms and Effects / G. Garab ed. Dordrecht, Boston, London: Kluwer Academic Publishers, 1998. V. IV. P. 2753-2756.

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EHFHGHKH<– 2006

36

Ihemq_ggu_j_amevlZluiha\heyxlk^_eZlv\u\h^qlhaZi_j_^Zqmkb]gZeZCa2+ \khk_^gxxde_ldmhl\_lkl\_ggZ^bnnmabyIP3q_j_as_e_\u_dhglZdluZaZkbgojhgbaZpbxm`_bf_xsbokykb]gZeh\Ca2+\^\mode_ldZo-^bnnmabyCa2+.

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1. >hdmdbgZ B<Fh^_ebjh\Zgb_ g_ebg_cghc ^bgZfbdb kb]gZevgh]h dZevpby \

de_ld_bfgh]hde_lhqguokljmdlmjZoK[hjgbdl_abkh\-cGZmqgh-l_ogbq_kdhcdhgn_j_gpbb©Fheh^_`v\gZmd_ªKZjh\-ghy[jyklj-51.

2. Lazrak A., Peres A., Giovannardi S., Peracchia C., 1994. Ca-mediated and independ-ent effects of arachidonic acid on gap junctions and Ca-independent effects of oleic acid and halothane. Biophys. J. 67, 1052-1059.

3. Rosenblum M.G., Pikovsky A.S., Kurths J., 1997. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78(22), 4193-4196.

535.33/34:621.373.826

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1. Tsien R.Y. (1998) Annu.Rev. Biochem. 67, 509–544. 2. Yang F., Moss L., and Phillips G.(1996) Nat. Biotechnol., 14, 1246–1251. 3. Mizuno H., Sawano A., Eli P., Hama H. & Miyawaki A. (2001) Biochemistry, 40,

2502–2510. 4. Cubitt A.B., Heim R., Adams S.R.,Boyd A.E., Gross L.A., and Tsien R.Y. (1995)

Trends Biochem. Sci.,20, 448–455. 5. M.G. Erickson, D.L. Moon and D.T. Yue (2003), Biophysical journal, 85, 599-611.

EHFHGHKH<– 2006

38

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2. E.M. Perdne and J.D. Rithie. Dissolved organic matter in fresh waters // Treatise on Geochemistry. 2003. V. 5. P. 273-318.

3. T.A.Dolenko, I.V.Fadeeva, S.A.Burikov, V.V.Fadeev, V.V.Chubarov. Determination of hydrology structures in seas and inner reservoirs using fluorescence characteristics of humic substance. In Proc. of III Intern. Conf. “Current Problems in Optics of Natu-ral Waters” (St.Petersburg, Sept. 12-16, 2005), 2005, pp. 241 – 248.

4. Filippova E.M., Fadeev V.V., Chubarov V.V.,Glushkov S.M., Dolenko T.A. Laser fluorescence spectroscopy as a method for studying humic substance. Applied Spec-troscopy Reviews, 2001, vp.p.87-117.

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EHFHGHKH<– 2006

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3. Denisov E.S., Emelianov S.V., Zatsepin A.G., Kremenetskiy V.V., Poyarkov S.G., Stroganov O.YU. The effect of bottom slope on the nearshore current in the rotating fluid (laboratory modeling). // “Fluxes and structures in fluids – 2005”.

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2. Caulliez G., Ricci N., Dupont R. On the coupling between the initial wind wave growth and the drift current structure.// in The air-sea interface. Eds. by Donelan M. A., Hui W.H., Plant W.J., The University of Toronto Press. Toronto. 1996. P. 27-34.

3. Huang N.E. Laboratory investigation of ocean surface roughness generation. //A.Brandt, S.E. Ramberg, M.F. Shlesinger (eds). Nonlinear Dynamics of ocean waves. World Scientific Press. 2001 Singapore. P. 128-149.

4. Zhang X., Harrison S. A laboratory observation of the surface temperature and ve-locity distributions on a wavy and windy air-water interface.// Phys. Fluids. 2004. V. 16. N1. P. L5-L8.

5. B\Zgh\ZBGF_evgbdh\ZHGBev]bkhgbkB<IhdZa__\D<>j_cnh\h_l_q_gb_gZ]eZ^dhcih\_joghklb\hû\ihlhd_\ha^moZBa\J:GNbabdZZlfhkn_jubhd_ZgZLK-856.

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2. Kelvin W. On stationary waves in flowing water. Philmag, ser.4, 42, 1871, 362. 3. Jeffreys H. On the formation the waves on water by wind. //"Proc Roy. Soc.".

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Theory and Practice. N.-Y.: Springer-Verlag Wien, 1992. 6. Davies K., Hartmann G.K. Radio Sci. 1997. V. 32. 1695. 7. Afraimovich E.L., Palamartchouk K.S., Perevalova N.P. Jour. Atm. Terr. Phys.

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1. Haag W., Karcher B., Strom J., Minikin A., Lohmann U., Ovarlez J., Stohl. Freezing

thresholds and cirrus cloud formation mechanisms inferred from in situ measurements of relative humidity //Atmos.Chem, Phys. 2003.V.3.P.1791-1806.

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1. Russell J.S. Report on waves. In : Rep. 14th Meeting of the British Association for

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4. ;_j_abgX:DZjifZg<B@WLN- 51, 1557 (1966) 5. Hammack J. L., Segur X. The Korteweg de Vries equation and water waves. Part 2.

Comparison with experiments. J. Fluid Mech., 65, 289 (1974). 6. E_\bq<=Nbabdh-obfbq_kdZy ]b^jh^bgZfbdZ=hkba^Zlnba-fZl ebl_jZlmju

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1. Walker, A. D. M., and H. Pekrides, Theory of magnetospheric standing hydro-magnetic waves with large azimuthal wave number. 4. Standing waves in the ring current region, J. Geophys. Res., 101, 27133–27147, 1996.Kfh^_ebjh\Zgguc

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74

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<jZ[hl_jZkkfhlj_gZf_lh^bdZkha^Zgby[b[ebhl_dbdhlhjZyijh\_jy_ljZaf_jfZkkb\Z\h\j_fydhfibeypbbb\u^Zzlhrb[dmdhfibeypbb\kemqZ_g_^hklZlhqgh]hjZaf_jZ\u^_e_ggh]h[mn_jZ>eyijh\_jdb\uiheg_gbymkeh\byfbgbfZevghg_h[oh^bfh]h jZaf_jZ fZkkb\Z bkihevam_lky fZdjhk BOOST_STATIC_ASSERT [b[ebhl_dbERRVWijbg_\uiheg_gbbdhlhjh]hdhfibeylhj\u^Z_lkhh[s_gb_h[hrb[d_LZdbfh[jZahfijh]jZffZkh^_j`ZsZylZdh]hjh^Zhrb[dmg_fh`_l[ulvaZims_gZlZddZdhgZ g_ [ueZ kha^ZgZLZd`_bkihevam_lkyrZ[ehgguc deZkk klZg^Zjlghc [b[ebhl_dbVWGQXPHULFBOLPLWVdhlhjuchij_^_ey_lk\hckl\Zp_euoqbk_elZdb_dZdfbgbfmffZdkbfmfdhebq_kl\h[blagZdh\mxijh\_jdm bdhgklZglmGLJLVWgm`gmxêy\uqbke_gbyfZdkbfZevghg_h[oh^bfh]hdhebq_kl\Z^_kylbqguopbnj\qbke_LZdbfh[jZahffh`ghhij_^_eblvnhjfmemjZaf_jZ[mn_jZêynhjfZlbjh\Zgbyp_eh]hqbkeZlbiZT iha\heyxsmxnhjfZlbjh\Zlv p_eh_ qbkeh lbiZT g_ [hykv \uclb aZ ]jZgbpufZkkb\Zg_aZ\bkbfhhljZaf_jZp_eh]hlbiZ int const SZ = std::numeric_limits<T>::is_signed + std::numeric_limits<T>::digits10 + 2; ;b[ebhl_dZ g_ iha\hey_l ijh]jZffbklm ^himklblv \hafh`ghklv \hagbdgh\_gby hiZkghc kblmZpbb \uoh

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g_kZgdpbhgbjh\Zgghfm ^hklmim d ^Zgguf kh klhjhgu aehmfure_ggbdh\ //Dh^ [b[ebhl_db #include <stdio.h> #include <cassert> #include <limits> #include <boost/static_assert.hpp> char const* get_sprintf_fmt(int const*) return "%d"; char const* get_sprintf_fmt(unsigned int const*) return "%u"; char const* get_sprintf_fmt(char const*) return "%c";

EHFHGHKH<– 2006

76

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template<class T> struct max_size; template<> struct max_size<int> typedef std::numeric_limits<int> lim; static std::size_t const value = lim::is_signed + lim::digits10 + 1;; template<> struct max_size<unsigned int> typedef std::numeric_limits<unsigned int> lim; static std::size_t const value = lim::is_signed + lim::digits10 + 1;; template<> struct max_size<char> static std::size_t const value = 1;; RZ[ehggucdeZkkRVWUHDP&DSDFLW\!bf__ljZagu_p_eb\h\j_fydhfibeypbb

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template<int Capacity> // Capacity - \f_klbfhklv struct ostream BOOST_STATIC_ASSERT(Capacity > 0); ?kebh[t_dl[ue kha^ZgijbnhjfZlbjh\Zgbbihke_^g_]h agZq_gbylhgZ^h

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char* start_; GZqZeh[mn_jZhldm^ZgZqg_lkynhjfZlbjh\Zgb_ ke_^mxs_]h agZq_gbyijb

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template<int Capacity, class T> ostream< Capacity - max_size<T>::value > operator<<(ostream<Capacity> os, T const& value) int n = sprintf(os.start_, get_sprintf_fmt(&value), value); assert(n <=

max_size<T>::value); return os.start_ + n; >ey[mn_jZbufjZaf_jZCapacity \ha\jZsZ_lh[t_dlostream<Capacity! mdZ

au\ZxsbcgZgZqZeh[mn_jZNhjfZlbjh\Zgb_h[uqghgZqbgZ_lkykwlh]h\uah\Z template<int Capacity> inline ostream<Capacity> out(char (&buf)[Capacity]) return ostream<Capacity>(buf); Gb`_ijb\_^zgijbf_jdhîhevah\Zl_eynhjfZlbjh\Zgbyp_eh]hqbkeZbih

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int i; std::cout<<"Enter an int:"; std::cin>>i;char buf[15];out(buf)<<i<<'\n';std::cout<< buf;

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EHFHGHKH<– 2006

78

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D1F = Hdhimax – Y, AD1 = ADmax, AF = 21

21 )()( FDAD − , KM = Hdhimax / tg (),

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λπ −∠−=∠ 'AKAAKD , ADmin = AD = AK*sin( AKD∠ ),

79

))**2/()arccos(( 2min

22 BDaADBDaABD −+=∠ ,

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−=∠ ,

))**2/())(arccos(( max22

max2 ACabACaBAC −+=∠ .

>ey.maxaZibr_f FADDAB ∠−∠= 2maxα ,

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gZ mjh\g_ klhygdb ihlj_[m_lky \uiheg_gb_ ke_^mxsbo h]jZgbq_gbc

maxmax βπγ ACB∠+≥ ]^_ ))**2/())arccos((( max222

maxmaxbACabACACB −+=∠ β

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))**2/())(arccos(( max22

max2

11 ACabACaACB −+=∠ ,

)/arcsin( max11 ADFDAFD =∠ , AFDACB 111 ∠+∠=α .

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EHFHGHKH<– 2006

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81

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g_f_kyqguoagZq_gbcl_fi_jZlmju <_klgbdFhkdh\kdh]hmgb\_jkbl_lZ 6, 2002.

3. Yu. P. Pyt’ev. Nonlinear reduction of a measurement. Math.Model, volume 1, number 5, p.44-59.

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EHFHGHKH<– 2006

82

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k = Tmax/tmin.

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>eymqzlZijhkljZgkl\_gghcoZjZdl_jbklbdbdZe_g^Zjgh]hieZgZijbkhklZ\e_gbbjZkibkZgbyijhkljZgkl\_ggZydhfihg_glZi_j_\h^blky\h\j_f_ggmxhi_jZlhjhf:KKJLZdgZijbf_jijbgZebqbbl_jjblhjbZevghm^Zezgguomq_[guodhjimkh\êyi_j_oh^Zbah^gh]hdhjimkZ\^jm]hcaZljZqb\Z_lkyg_dhlhjh_\j_fyLZdh_\j_f_ggh_h]jZgbq_gb_h[oh^ylke_^mxsbfh[jZahfijbi_j_]jmiibjh\d_ij_^f_lh\ih\_jrbgZf^_j_\Z\u[bjZ_lky]em[bgZg_dhlhjhc\_jrbgukhhl\_lkl\mxsZyhij_^_ezgghfm\j_f_gghfmbgl_j\ZemgZijbf_ji_j_ju\mgZh[_^>Zgguc\j_f_gghcbgl_j\Zeh[hagZqZ_lky\\b^_ ©imklhcª aZ^ZqbgZ\uiheg_gb_dhlhjhcgZagZq_gg_dhlhjuc ©mgb\_jkZevgucªbkihegbl_evg_bf_xsbcgbdZdboh]jZgbq_gbcghijbkhjlbjh\d_^ZggZy \_jrbgZ aZgbfZ_l nbdkbjh\Zggmx ]em[bgm LZd`_ \\h^ylky ^jm]b_ bgl_j\Zeu\j_f_gb–g_[hevrb_i_j_ju\uf_`^miZjZfb–\\b^_z©imkluoªaZ^Zq

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K=d*k.

Hq_\b^ghqlhN<<K,bgZq_j_r_gb_^ZgghcaZ^Zqb[m^_lg_^hklb`bfuf Kmqzlhf©imkluoªaZ^Zqihemqbfgh\mx]em[bgm]jZnZ

Kiheg. = d * Tmax/tmin + z

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Graphêydhlhjh]hkms_kl\m_lba\_klgucZe]hjblflhiheh]bq_kdhckhjlbjh\dbhibkZgguc\khhl\_lkl\mxs_cebl_jZlmj_>@

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NZdlhjuijhp_kkZkihfhsvxdhlhjuoj_Zebam_lkyaZ^Zggucl_ogheh]bq_kdbcj_`bf.

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EHFHGHKH<– 2006

84

Kh\hdmighklvfgh`_kl\ZnZdlhjh\fgh`_kl\Zp_e_\uonmgdpbcbfgh`_kl\Zfh^_e_cfh`_l[ulvgZa\ZgZl_ogheh]bq_kdhckblmZpb_c>eyl_ogheh]bq_kdhckblmZpbbg_h[oh^bfhihkljh_gb_fh^_eblZddZdl_ogheh]bq_kdZykblmZpby[_afh^_ebg_fh`_l[ulvmijZ\ey_fZbg_ij_^klZ\ey_lijZdlbq_kdh]hbgl_j_kZ

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y = f(x1, x2, … , xn),

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m 3o1o2).

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Z1 + 2Z2 + 4Z3 = C1 + 2C2 + 4C3,

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EHFHGHKH<– 2006

86

Kms_kl\mxl ijhp_^mju ^jm]h]h lbiZ:[hg_glh\ jZkij_^_eyxl fZjd_lbg]h\ufdZl_]hjbyfDZaZehkv[uih^h[gh_jZa^_e_gb_^he`ghhkms_kl\eylvkybkdexqbl_evgh\aZ\bkbfhklbhllZjbnguoieZgh\dhlhju_jZa^_eyxlkygZ©fZkkh\u_ªwlhgZijbf_jlZjbnu[_aZ[hg_glkdhcieZlu©dhjihjZlb\gu_ªkhhl\_lkl\_gghhjb_glbjh\Zggu_gZdhjihjZlb\guoZ[hg_glh\©9,3ªbl^H^gZdh\hafh`gukblmZpbbdh]^ZZ[hg_glbf_xsbc©fZkkh\ucªlZjbngucieZgbf__llZd`_b_`_f_kyqgu_gZqbke_gbydhlhju_ij_\hkoh^yl lZdh\u_mbguoZ[hg_glh\ ©9,3ª[he__lh]hlZdb_kemqZbg_j_^dbbihwlhfm hlg_k_gb_ lZdh]h Z[hg_glZ dfZkkh\hfm k_]f_glmjugdZ[ueh[uhrb[hqguf

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Nkj = (Ni + Ni-1) / 2 Kkq = (Ni / :i + Ni-1 / :i-1 ) / 2.

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88

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LZdbfh[jZahfihdZaZghdZdh^ghmkljhckl\hiha\hey_le_]dhb[ukljhkdhgkljmbjh\ZlvjZaebqgu_wdki_jbf_glZevgu_mklZgh\dbj_rZyl_fkZfufaZ^Zqmkha^Zgbyijhklh]hmkljhckl\Zêyijh\_^_gbywdki_jbf_glZevguojZ[hlq_j_aBgl_jg_l 1. I.V. Yaminsky, A.S. Filonov, A.V. Bolshakova, M.O. Gallyamov, O.I. Kiselyova, 2. A.V. Shishlova. Internet Outlook into the Microworld: From Atoms and Molecules

to Living Cells. Proceedings of the European Distance Education Network – Lo-monosov Moscow State University Conference "Information and Communication Technologies and Human Resources Development: New Opportunities for Euro-pean Co-operation. 3-5 October 1999, Moscow, Russia. p. 236-237.

3. A. V. Bolshakova, A .S. Filonov, M. O. Gallyamov, D. Yu. Gavrilko, E. V. Du-brovin, O. I. Kiselyova, A. M .Lomonosov, E. B. Meshkov, I. V. Yaminsky. Open Experimental Internet Practical Studies in Nanoscopy of Polymers and Biomacro-molecules. Phys. Low-Dim. Struct., 3/4, 113-118 (2003).

4. A.V. Bolshakova, N.I. Nikanorova, I.V. Yaminsky. Practical studies in nanoscopy of blockcopolymers. MSU. 2002 – 16 p.

EHFHGHKH<– 2006

96

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Fh`_lqblZlvbaZibku\Zlvbah[jZ`_gby\hfgh]bonhjfZlZo\dexqZyFIT, FF, IMG, TIF, JPG, BMP, JPG. 1. JZ^bh]jZnbyK[klZl_cFE<LZjZkh\ 2. Mikerov V.I., Zhitnik I.A., Korneev V.V., Pertsov A.A., Tindo I.P., Ignat’ev A.P.,

Tukarev V.A. and Waschkowski W. A two-coordinate high-resolution detector for registering thermal neutron images. J. Moscow Phys. Soc., 2 (1992) 181-188.

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1. =hgkZe_kJ<m^kJPbnjh\Zyh[jZ[hldZbah[jZ`_gbc–FL_oghkn_jZ 2. Pitas I., Venetsanopoulos A. Nonlinear Digital Filters: Principles and Applications.

- Boston, MA: Kluwer, 1990. 3. Wang Z., Zhang D. Progressive Switching Median Filter for the Removal of Impulse

Noise from Highly Corrupted Images // IEEE Trans. Circuits Systems – II. 1999. V. 378-80.

4. Zhang D., Wang Z. Impulse Noise Detection and Removal Using Fuzzy Techniques // Electron. Lett. 1997. V. 33, P. 378-379.

5. Kong H., Guan L. A Neural Network Adaptive Filter for the Removal of Impulse Noise in Digital Images // Neural Networks. 1996. V. 3-378.

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e-mail: [email protected] 1. B.Esser,V.Rzhevskii.Phys.Rev.B 72, 012410, (2005). 2. G.Suciu, J.C.Toussaint, J.Voiron. Journal of Magnetism and Magnetic Materials,

240, 229, (2002). 3. N.S.Almeida, D.L.Mills. Phys.Rev.B 52, 13504, (1995).

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[email protected] 1. :*UDQRYVN\DQG0,QRXH-0DJQ0DJQ0DW272-276, Suppl. 1 (2004) E1601. 2. I.V. Bykov, E. A. Ganshina, V.S. Guschin et al., Phys. of Solid State 47 (2005) 281. 3. Ju. V. Boriskina, S. G. Erokhin, A. B. Granovsky et al., Phys. of Solid State (2006)

N4. 4. G. T.Ruck, D. E. Barrick, W. D. Stuart, C. K. Krichbaum, Radar Cross Section Hand-

book Plenum Press N.Y. 1970.

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1. M. Komuro, M. Hanazano, and Y. Sugita, J. Appl. Phys. 67 (1990) 5126 2. Y. Sugita et al., Appl. Phys. 70 (1991) 5977 3. M.A. Brewer, C.J. Echer, and K.M. Krishnan, J. Appl. Phys. 81 (1997) 4128 4. M. Takashi, T. Shimatu, IEEE Trans. Magn. 26 (1990) 1485 5. J.O. Rantschler and C. Alexander, Jr., , J. Appl. Phys. 93 (2003) 6665 6. I.T. Iakubov et al., J. Magn. Mater. 272-276 (2004) 2208

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E–mail:[email protected]

1. ;Wkk_j<<J`_\kdbcBa\<mah\IG> ,12, 38. (2004). 2. B. Esser, V.Rzhevskii, Phys.Rev. B 72, 012310, (2005). 3. G.Suciu, J.C.Toussaint, J. Voiron, J. Magn. Magn. Mater. 240 , 229, (2002).

567.611.4

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EHFHGHKH<– 2006

124

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126

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EHFHGHKH<– 2006

128

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( )2/1||)( −= xOxu , ( )2/1||)(||

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xoxikux

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′=∂

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129

∫ =n

n

b

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^j_cnh\Zebdp_gljmkehyLZdbfh[jZahfjZkkfhlj_gZfh^_evk`Zlbylhdh\h]hkehy . 1. ::<eZkh\³H\b[jZpbhgguok\hckl\Zowe_dljhggh]h]ZaZ´@WLNL<ui

(1938) 2. E.G.Harris “On a plasma sheath separating regions of oppositely directed magnetic

field.” Nuovo Cimento 23.115 (1962) 3. Y.Asano “Current sheet structure around the near-Earth neutral line observed by Geo-

tail” Journal of Geophysical Research vol. 109 (2004) 4. Y.Asano “Evolution of the thin current sheet in a substorm observed by Geotail ”

Journal of Geophysical Research vol. 108 (2003) 5. D.Nunn “A Novel Technique for the Numerical Simulation of Hot Collision-Free

Plasma; Vlasov Hybrid Simulation.” Journal of computational physics 108, 180-196 (1993)

6. @Q;w^k_e :E_g]^hg ³NbabdZ ieZafu b qbke_ggh_ fh^_ebjh\Zgb_´Fhkd\ZWg_j]hZlhfba^Zl

7. M. Hodhino. “Electron Surfing Acceleration in Magnetic Reconnection” 8. Michael Hesse, Dan Winske, Masha Kuznetsova . “Hybrid Modeling of the Formation

of Thin Current Sheets in Magnetotail Configuration” J. Geomag. Geoelectr., 48, 749-763, (1996)

9. >:<Iheydh\ ³Qbke_ggh_bgl_]jbjh\Zgb_mjZ\g_gbc^\b`_gby\ijbf_g_gbbd mkdhj_gbx qZklbp ieZafu \ fh^_eb ^bgZfbq_kdh]h lhdh\h]h kehyKujh\Zlkdh]h´NbabdZIeZafulhfk-665 (2004)

10. B.U.O. Sonnerup. “Adiabatic Particle Orbits in a Magnetic Null Sheet”. Journal of Georhysical Research. Vol. 76, NO. 34. December 1, (1971).

11. :::jk_gv_\³E_dpbbhdbg_lbq_kdbomjZ\g_gbyo´FGZmdZ1992 12. [Rober M.Strain. “The Vlasov-Maxwell-Boltzmann system in the whole space”.

arXiv:math.AP/0512002 v2 13 Feb 2006

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5. Faure Ph., Korn H. A new method to estimate Kolmogorov entropy from recurrence plots: its application to neural signals// Physica D. 1998. V. 122. P. 265.

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1. Sonnerup, B.U.O., “Adiabatic particle orbits in magnetic null sheet” // J. Geophys. Res., 1971, v.76, p.8211.

2. Chen J. and P. J. Palmadesso “Chaos and nonlinear dynamics of single-particle orbits in magnetotaillike magnetic field” // J. Geophys. Res, 1986, v.91, p.1499

3. Hoshino M., A. Nishida, T. Mukai, Y. Saito, and T. Yamamoto “Structure of plasma sheet in magnetotail: double-peaked electric current sheet” // J. Geophys.Res., 1996, v.101 p.24775.

4. Asano, Y., T. Mukai, M. Hoshino, Y. Saito, H. Hayakawa, and T. Nagai “Evolution of the thin current sheet in a substorm observed by Geotail” // J. Geophys. Res.,2003, v.108,p.10101.

5. Buchner J., and ZelenyiL.M “Regular and chaotic charged particle motion in magneto-taillike field reversals, Basic theory of trapped motion” // J. Geophys. Res., 1989,v.94,p.11821.

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1. Munevar, S., Y. L. Wang and M. Dembo (2001a). Distinct roles of frontal and

rear cell-substrate adhesions in fibroblast migration. Mol. Biol. Cell 12, 3947-3954.

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chemotaxis of sea urchin sperm”. Nature Cell Biology, 2003, vol.5, p.109 – 117.

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E–mail:[email protected] 1. Funke, H., A. Sheinost and M.V.

Chukalina. 2005. Phys. Rev. B (In press).

2. Grossmann, A. and J. Morlet. 1984. SIAM J. of Math. Anal. 15, 723-728. 3. Sayers, D.E.; E.A. Stern and F.W. Lytle. 1971. “New Technique for Investigating No

crystalline Structures: Fourier Analysis of the Extended X-Ray—Absorption Fine Structure”. Phys. Rev. Lett. 27, 1204-1207.

4. Stern, E.A.; D.E . Sayers and F.W. Lytle. 1975. “Extended X-ray absorption fine structure technique. III. Determination of physical parameters”. Phys. Rev. B 11, 4836-4846.

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EHFHGHKH<– 2006

162

10-3

10-2

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100

101

102

O2 +

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2O

2 + O

2+

O2 +

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2O

2 + O

-

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+ O

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O2 +

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2

HO

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OH

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O2

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OH

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3

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+ 2

O 2

O2 +

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Jbk M=3, t fdk X kf

EHFHGHKH<– 2006

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MATHEMATICAL MODELING OF TURBULENCE IN HOMOGENEOUS FLOWS

Terentiev Leonid

Friedrich-Alexander University Erlangen-Nuernberg, Institute of Fluid Mechanics, Germany

Turbulence is the most complicated kind of fluid motion, but, at the same time, it is the most common one. Complex turbulent structures exist on all scales from the flow in cup of tee to the motion of galaxies. Besides being an intriguing scientific challenge, the under-standing of turbulence origin and ability to accurately predict it is a necessity and prerequisite for resolving many technological and environmental problems. Despite century long research, turbulence modeling remains still the greatest challenge in modern hydromechanics. Navier (1821) formulated a general set of equations governing the motion of all fluids, which is the foundation of the modern fluid dynamics. This implies that turbulence is the general solution of the Navier-Stokes system. Nevertheless, its application to the real turbulent flows is practi-cally impossible because of the high computational requirements, which cannot be supplied even with the modern computers. In order to overcome this problem the statistical approach, suggested by Reynolds (1895), is employed. There each flow variable is separated into the mean and fluctuating components. The resultant equations, called the Reynolds-averaged sys-tem, give an access to the flow properties and have feasible computational costs

179

Because of the nonlinearity of this system, an additional unknown term uiuj, called the Reynolds tensor, appears in the mean momentum conservation law. It acts as an additional stress and characterizes the effect of the turbulence. Because of its presence the resultant system is not closed until the number of unknowns equals the number of equations, so that it can be solved nu-merically. The fundamental goal of the turbulence modeling is to hypothesize a modeling rela-tionship that ties the Reynolds stress tensor to the mean flow quantities in a physically consistent way. In the current work the class of so called second-order closures is considered, where all components of the Reynolds tensor are calculated using partial differential equations

The main objective of the current work is derivation of the turbulence model account-ing for flow anisotropy and based on this system. The principal ability of the proposed ap-proach to deal with anisotropy is of particular importance in a great variety of flows. The de-rived efficient numerical method shows a capability to predict a number of benchmark flows like a strained-, rotated- and sheared- anisotropic homogeneous turbulence. All these predic-tions are in a good agreement with the experimental data. While a considerable work still has to be done to expand the models abilities and validate its performance, the first phase has demonstrated the potential of the proposed approach to predict flows of engineering interest.

E–mail: [email protected] 1. Jovanovic, J. (2004) The statistical dynamics of turbulence. 2. Terentiev, L. (2006) The turbulence closure model based on linear anisotropy invari-

ant analysis // PhD dissertation, Institute of Fluid Mechanics, Friedrich-Alexander University Erlangen-Nuernberg.

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1. Shpyrko O., Huber P., Grigoriev A., Pershan P.S., Ocko B., Tostmann H., Deutch M.

Phys. Rev. B 67, 115405 (2003) 2. Mora S., Daillant J., Mecke K., etc., Phys. Rev. Lett. 90, 216101 (2003) 3. Buff F.B., J. Chem. Phys. 19, 1951 (1951) 4. Mecke K., Dietrich S., Phys. Rev. E 59, 6766 (1999) 5. Tolman R.C., J. Chem. Phys. 17, 333 (1949) 6. Zon B.A., Dorofeev D.L., Dolgikh A.V. Phys. Rev. E. 67, 056311 (2003).

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[email protected] 1. Giulio Cerullo and Sandro De Silvestri, “Ultrafast optical parametric amplifiers,” Re-

view of scientific instruments, 74, No.1 (2003). 2. Brodeur, S.L. Chin, “Ultrafast white-light continuum generation and self focusing in

transparent condensed media”, J. Opt. Soc. Am. B 16, 637 (1999). 3. T. Ditmire et al. “Effects of cubic nonlinearity on frequency doubling of high-power

laser pulses”, J. Opt. Soc. Am. B 13, 649 (1996).

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Liu, J.-F. Gravel, G. Roy, S.L. Chin, Appl. Phys. B, 82, pp. 111 – 122. 2. V.P. Kandidov, N.Aközbek, M. Scalora, O.G. Kosareva, A.V. Nyakk, Q. Luo,

S.A. Hosseini, S.L. Chin., Appl. Phys. B, 80, pp. 267 – 275. 3. <IDZg^b^h\G:]ha[_dFKdZehjZH=DhkZj_\Z:<GyddQEmhK:

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W. Liu, J. Gravel, S.L. Chin, Proc. SPIE, 5708, pp. 91 – 101.

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3. Nakayama H., Saiton K., Sakashita M., Ishii K., Nishikawa K. Chemical Physics Let-ters, 320, 2000, 323-327.

4. V.G.Arakcheev, V.N.Bagratashvili, A.A.Valeev, V.M.Gordiyenko, V.V.Kireev, V.B.Morozov, A.N.Olenin, V.K.Popov, V.G.Tunkin and D.V.Yakovlev. Linewidths and shifts of carbon dioxide CARS spectra near the critical point. J.Ram.Spectr., 34, 952-956 (2003)

5. V.Morozov, S.Mochalov, A.Olenin et al. J.Ram.Spectr., 34, 983-988 (2003)

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1. :g^j__\:<³<aZbfh^_ckl\b_ZlhfZkhk\_jokbevgufbiheyfb´@?LN

l\uik-806. 2. A.V. Andreev, O.A. Shoutova “Single hydrogen like atom ionization by ultrastrong

laser field: Nonperturbative approach”, Physics Letters A, 2006, v. 350, Issues 3-4, p.309-314.

3. Ganeev R.A., Baba M., Suzuki M., Kuroda H. “High-order harmonic generation from VLOYHUSODVPD´3K\VLFV/HWWHUV$9- p.103-109.

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1. 1. S. Flach and C. R. Willis, Phys. Rep. 295, 181 (1998); S. Flach, Computational

studies of discrete breathers, in "Energy Localization and Transfer", Eds. T. Dauxois, A. Litvak Hinenzon, R. MacKay and A. Spanoudaki, World Scientific, pp.1-71 (2004).

2. G.M. Chechin, G.S. Dzhelauhova, E.A. Mehonoshina. Breathers or quasibreathers? Arxiv: nlin.ps/0601034 (submitted to Phys.Rev.E).

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1. Arbore M.A., Marco O., Fejer M.M. (1997) Opt.Lett. LK. 865. 2. Arbore M.A., Galvanauskas A., et.al. (1997)Opt.Lett.LK. 1341.

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1. Braun A., Korn G., Liu X., Du D., Squier J., Mourou G. // Opt. Lett., 1995. V. 20. P.

73. 2. Nibbering E.T.J., Curley P.F., Grillon G., Prade B.S., Franco M.A., Salin F., Mysy-

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Lett., 1997. V. 22. P. 304. 4. Re_gh\K:DZg^b^h\<IHilbdZZlfhkn_jubhd_ZgZLK

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1. R.J.Tompkins, I.P.Mercer, M.Fettweis, C.J.Barnett, D.R.Klug, Lord G.Porter, I.Clark, S.Jackson, P.Matousek, A.W.Parker, and M.Towrie “5-20 keV laser-induced x-ray generation at 1 kHz from a liquid-jet target”// Rev. of Scientific Instr., 69, 3113-3117 (1998)

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2. T. Barret, P. Lang, J. Watterhouse, J. Cook, S. Cullicon, B. Fuller, S. Telles, J. Pull-man. Non-destructive measurement of gelatin and calcium content of european papers: 1400-1800. ERICE 96. International conference on conservation and restoration of ar-chive and library materials. Pre-prints, vol. 2. Rome (1996) p. 517-534.

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1. FNjZgkhgNZah\h-dhgljZklguc b bgl_jn_j_gpbhgguc fbdjhkdhiu i_j knjF

2. M.Totzeck, H.J.Tiziani, “Phase singularities in 2D diffraction fields and interference microscopy ”, Opt.Comm. 138, pp.365-382 (1997)

3. 97\FKLQVN\$7DYURY'6KHSHOVN\_WDO7KUHH-dimensional living cell imaging with high spatial and time resolutions. Holography, Interferometry, and Optical Patt.Recogn. in Biomedicine II; Los Angeles, CA; USA; 23-24 Jan. 1992. pp. 96-100. 1992

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5. V.A. Andreev, K. V. Indukaev. The problem of subrayleigh resolution in interference microscopy, J. of Russian Laser Research, V. 24, November 3, 2003.

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1. Brazhnikov D.V., Taichenachev A.V., Tumaikin A.M. and Yudin V.I., J. Opt. Soc. Am. B 22(1), 57-64 (2005).

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1. Yu.K Voronko, A.A. Sobol, A. Ya. Karasik et al. // Optical materials 20 (2002) 197-209.

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1. Introduction to uClinux STAMP Board Documentation Coursework and Lab Materi-als // Analog Devices Inc.

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1. R. H. Friend and A. D. Yoffe. (1987) Adv. Phys. 36, 2. 2. L. Kulyuk, L. Charron and E. Fortin. (2003) Phys. Rev. B 68, 075314.

THE PROBLEM OF FIELD CAUSALITY IN THE PROCESS OF SPONTANEOUS EMISSION OF TWO RADIATORS AT THE INITIAL

STAGE OF EMISSION

Galeamov E.

Institute of Applied Physics, Academy of Sciences of Moldova,

The processes of collective spontaneous decay of time-dependent quantum systems and the formation of two photons as a wave packets are of great interest to quantum optics. The first report on non-exponential spontaneous decay of quasi-stationary states can be found in the work of Khalfin [1], who demonstrated, that the corrections to the exponential law of spontaneous decay behave like 1/t, with t the time, basing his reasoning on the fact that the energy distribution density is semi-finite. Simultaneously with the development of model atom-field interaction Hamiltonians more exact expressions for the corrections to the expo-nential spontaneous decay law appeared in the literature [2,3]. The papers of Wilkievicz and Eberly and Atkins and Wooloy [4,5] should also be mentioned, since the researchers point to the need to allow for the time lag within the atom when the corrections to the exponential law are taken into account.

The equation for the mean value of the population difference has been obtained. This equation implies that the emerging wave packets (photons) in the time interval t~1/& has a strong effect not only on the excited state of the radiators (atoms, nuclei) but also on the ground state [6]. The coefficient of the stimulating action of the emerging photon field is of the same order of magnitude as the spontaneous transition coefficient.

In this report a theory that describes the spontaneous decay of two hydrogen-like at-oms on time scales that are small or large compared to the reciprocal photon emission fre-quency is proposed. On short time scales the spontaneous decay rate is found to tend in an os-cillatory manner to the exponential law of spontaneous decay. The process of energy ex-change in time and space between two radiators placed at the distance D is discussed. The be-havior of non-locality of electromagnetic field in the process of spontaneous emission is ob-served. This effect gives us non-causality terms in the exchange integrals between these radia-tors. In order to take into account all specific properties of quantum non-locality of two radia-tors located on distance D, it is proposed the technique of elimination of electromagnetic field operators without dipole approximation of these radiators in interaction with the field. The system of equations, which describes the interaction of radiators with vacuum of electromag-netic field, is obtained. The interaction rate coefficients strongly depend on time taking into account causality and non-causality energy exchanges between the radiators. The behavior of this system of radiators at short times and the long times in comparison with D/c is carefully studied. The entanglement behavior of atomic states in process of spontaneous emission as function of time is found. The corrections to spontaneous emission times and cooperative

EHFHGHKH<– 2006

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emission times are studied. The specific problem appears in the moment when retardation ef-fects occur in the moment when time achieves value D/c. In this case retardation flux achieved the second atom in the classical and non-classical effects work together in the accel-eration rate of collective spontaneous emission.

[email protected]

1. L.A. Khalfin Dokl.Acad.Nauk SSSR 111, 345 (1956) [Sov. Phys. -- Dokl.1, 671(1956)]; 115, 2770 (1957) [2, 340 (1957)], Zh. Eksp. Teor. Fiz. 33, 1351 (1957) [Sov. Phys. --JETP 6, 1053 (1958)].

2. P.W. Millonni and P.L. Knight. Phys. Lett. A 56, 275 (1976). 3. L.Davidovich and H.M. Nussenzeig, in: Foundation of Radiation Theory and Quan-

tum Electrodynamics, ed. by A.O.Barut, Plenum, New York (1980). 4. K.Wilkievich and J.H. Eberly. Ann. Phys. 101, 574 (1976). 5. J. Seke and W.N. Herfort. Phys. Rev. A 38, 833 (1989); Ibid, 40, 1926 (1988). 6. N.A. Enaki, JETP 82, 607-615 (1996).

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[email protected]

1. Erdal Dinc Dumitru Baleanu, A new fractional wavelet approach for the simultane-ous determination of ampicillin sodium and sulbactam sodium in a binary mixture, Sience direct (2005)

2. I.Daubechies, Ten lectures on wavelets, New York (1992). 3. F:klZnv_\Z<_c\e_l-ZgZebahkgh\ul_hjbbbijbf_juijbf_g_gbyMki_obnbabq_

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[email protected]

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1. :eb\_j^b_\::Bkihevah\Zgb_ki_dljZkdhjhkl_cêyijhkljZgkl\_ggh-\j_f_ggh]hbkke_^h\Zgby\ukhdhkdhjhklguoijhp_kkh\@LN67k-134.

2. Aliverdiev A. (2002) Applications of the time-resolved integral-geometric methods for the composite materials diagnostic // Scientific Israel–Technological Advantages, 4, p.108-111.

3. Aliverdiev A., Caponero M., Moriconi C. (2003) Speckle-velocimeter for robotized vehicles // Proc. of SPIE, 5147, p. 140-147.

4. Aliverdiev A., Batani D., Malka V., et al. (2005) Time-Resolved Analysis of High-Power-Laser Produced Plasma Expansion in Vacuum irradiation // in the Book of Proc. of Int. Simp. on RGD (Bari, Italy, 2004) / Edited by M. Capitelli. Melville, New York, p.419-424.

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1. Lugovtsov A.E., Priezzhev A.V., Tyurina A.Yu., Koshelev V.B., Fadyukova O.E. Rheological behavior of erythrocytes of hemorrhagic rats: examination by the method of laser diffractometry. //Optical Technologies in Biophysics and Medicine V, Tuchin V.- Ed, SPIE Proc., 2003, v. 5474, pp. 200-203.

2. Lugovtsov A.E., Priezzhev A.V., Tyurina A.Yu, Koshelev V.B., Fadyukova O.E. La-ser diffractonetry of rheological behavior of erythrocytes of rats with experimentally induced ischemia: effect of semax. //Proc. of OSAV’2004, The International Topical Meeting on Optical Sensing and Artificial Vision – Saint Petersburg: ITMO State University, 2004, pp. 241 – 248.

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1. Ihnatouski M.I., Sviridenok A.I. The contact problem on a metal indentor penetration into a strongly Rough polymer surface. // Proc. of the Second Int. Conf. On Engineer-ing Rheology, Zielona Gora, Poland, 24-27.08.2003. International Jornal of Appleid Mechanics and Engineering, 2003, V.8

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4. Kd\hjph\><Debgbq_kdbcZgZeba^\b`_gbcZgZebaihoh^dbFk 5. Orlin MN, McPoil TG Plantar pressure assessment.// Physical Therapy// vol.80

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EHFHGHKH<– 2006

250

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Ih^k_dpby F:L?F:LBQ?KDH=HFH>?EBJH<:GBY klj-157 :G:EBA<GMLJ?GG?C=B>JH>BG:FBDB:F?;HB>GHCDE?LDB **IZ\eh\ZL:LhdZjqmd:<PmdZgh\::.................................................................................144 FH>?EBJH<:GB? <GMLJBDE?LHQGHC KB=G:EBA:PBB KI?JF:LHAHB>: FHJKDH=H?@:<IJHP?KK?O?FHL:DKBK: **FbkxlbgZLK>hdmdbgZB<......................................................................................................145 F:L?F:LBQ?KDH? FH>?EBJH<:GB? <A:BFH>?CKL<BY <KLJ?QGUO WE?DLJH-F:=GBLGUO <HEG < :DLB<GHC KJ?>? IHEMIJH<H>GBDH<H=H HILBQ?KDH=HMKBEBL?EY :diZjh\<<R_gbgN: ...............................................................................................................146 HILBFBA:PBYDHGKLJMDPBBF:=GBL:K-LBI:>EYLJ:KKUIJH<H>DBIMQD:P?GLJ:IJHLHGGHCEMQ?<HCL?J:IBB Q_jguo:GEZjbhgh\<I............................................................................................................148 :E=HJBLFUK=E:@B<:GBYBNBEVLJ:PBBWDKI?JBF?GL:EVGUO>:GGUO ?]hjh\<< .........................................................................................................................................149 H<U;HJ?I:J:F?LJH<F?LH>:IHBKD:KLJMDLMJGUOFH>?E?CG:GHQ:KLBPIH>:GGUFF:EHM=EH<H=HJ:KK?YGBY <hedh\<<IZjZohgkdbc=< .......................................................................................................151 <WC<E?L-:G:EBAB?=HIJBF?G?GB?(;$)6KI?DLJHKDHIBB RZ[_evgbdh\ZKEQmdZebgZF< ................................................................................................152 J?DHGKLJMDPBY BAH;J:@?GBC < :LHFGH-KBEH<HC FBDJHKDHIBB KBKIHEVAH<:GB?F<?C<E?L-:G:EBA: **Njheh\Z=<Kb[]ZlmeebgFW;hg^Zj_\Z?:=Zebfmeebg >AKZeZoh\FO .............................................................................................................................153 HP?GD: D:Q?KL<: PBNJH<UO BAH;J:@?GBC A:DH>BJH<:GGUO IH :E=HJBLFM SPIHT <hehoh\<:Gh\hk_eh\K:..........................................................................................................154 BKKE?>H<:GBY K<HCKL< IHEYJBAH<:GGH=H K<?L: ;?ABG?JPBHGGUF F?LH>HF >y]be_\ZGF ....................................................................................................................................155 BKIHEVAH<:GB?KI?DLJH<<UKHDH=HJ:AJ?R?GBYBL?DKLMJUBAH;J:@?GBY>EY MEMQR?GBY DE:KKBNBD:PBB KI?DLJHAHG:EVGUO BAH;J:@?GBC E?KGUOL?JJBLHJBC *O\Ze_cK<........................................................................................................................................156 Ih^k_dpby FHE?DMEYJGHCNBABDB klj-181 BKIHEVAH<:GB?><HCGHCFH>MEYPBB<BAF?J?GBBDHWNNBPB?GL:L?IEH<H=HJ:KRBJ?GBYIJH<H>YSBO@B>DHKL?C Kh[he_\Z:<DZjq_\kdbcHH ......................................................................................................158 IJHF?@MLHQGUC F:DKBFMF G: DJB<HC J:>B:EVGH=H J:KIJ?>?E?GBY<H>UB?=HK<YAVKLHIHEH=B?CK?LDB<H>HJH>GUOK<YA?C<<H>? **Kheh\_c:; ....................................................................................................................................160

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252

BHGGU? @B>DHKLB IHQ?FM HGB Y<EYXLKY OHJHRBFB J:KL<HJBL?EYFB>EYJ:AEBQGUO<?S?KL< :wjh\:: ..........................................................................................................................................161 <EBYGB? =:AH<H=H J:AJY>: G: IJHP?KK <HKIE:F?G?GBY <H>HJH>GH-DBKEHJH>GHCKF?KB DhgklZglbgh\kdbcJKRb[dh\<F ............................................................................................161 KDHJHKLVA<MD:BJ:>B:EVG:YNMGDPBYJ:KIJ?>?E?GBY GbdheZ_\ZHI...................................................................................................................................162 BKKE?>H<:GB? <A:BFH>?CKL<BY BFIMEVKGH=H IH<?JOGHKLGH=H J:AJY>:KIEHKDHCM>:JGHC<HEGHC *AgZf_gkdZyB:B\Zgh\BWHjeh\>F ...................................................................................163 H <HAFH@GHKLB IJBF?G?GBY BFIMEVKGHC IE:AF?GGHC KLJMB >EY<HKIE:F?G?GBY<HA>MRGH-IJHI:GH<HCKF?KB DZf_gsbdh\K:Dhe_kgbdh\?;Eh]mgh\:: ........................................................................166 IJH>HEVGH-IHI?J?QGUCJ:AJY><K<?JOA<MDH<HFIHLHD?<HA>MO: Dhe_kgbdh\?;Eh]mgh\:: ........................................................................................................166 IJHKL?CRB?FBDJHEHDHFHLBEYI?J?><B@?GBY<<YADBO@B>-DHKLYO K_e_ag_\:: .....................................................................................................................................167 DE:KL?JGUCIH>OH>DBAMQ?GBXN:AH<H=HIH<?>?GBYM=E?<H>HJH>H< HaZjgh\B:.........................................................................................................................................16 H KI?DLJ:EVGUO O:J:DL?JBKLBD:O A<MDH<UO <HEG BAEMQ:?FUO <BOJ?<UFBDHEVP:FB DmavfbgI: ......................................................................................................................................169 IJBF?G?GB? F?LH>: IK?<>HDH=?J?GLGUO KHKLHYGBC >EY J:KQ?L:KI?DLJH<IH=EHS?GBYHAHG: FZeuobg?FEhiZ_\><GZfbhl<: ......................................................................................171 WDKI?JBF?GL:EVGH? BKKE?>H<:GB? KI?DLJ: IH=EHS?GBY <HA;M@->?GGH=HHAHG:<GBADHL?FI?J:LMJGHCIE:AF? FZeuobg?FAujygh\KFEhiZ_\>< ....................................................................................172 KI?DLJHKDHIBYF?L:KL:;BEVGH=HKHKLHYGBY %*FHE?DMEDBKEHJH>:<IE:AF?BAF?J?GB?=:AH<HCL?FI?J:LMJU Aujygh\KFEhiZ_\><FZeuobg?F ....................................................................................173 G?KL:PBHG:JG:Y G?MKLHCQB<HKLV =,JLE?J: IH=J:GBQGH=H KEHY G: <H=GMLHCKL?GD?WDKI?JBF?GLBL?HJBY **;hcdh:<B\Zgh\:<DZqZgh\XKFbs_gdh>: ............................................................175 HILBFBA:PBYL?IEHH;F?G:<DHEHKGBDH<HFOHEH>BEVGBD? Gh\hkzeh\:= ...................................................................................................................................176 <EBYGB? NBABQ?KDBO I:J:F?LJH< LHIEB<GH-<HA>MRGHC KF?KB < FHF?GL <HKIE:F?G?GBY G: KDHJHKLV J:KIJHKLJ:G?GBY IE:F?GB <HKGH<GHCN:A?K=HJ:GBY Kfhe_gkdbc<<>y]be_\ZGF .....................................................................................................177 MATHEMATICAL MODELING OF TURBULENCE IN HOMOGENEOUS FLOWS Terentiev Leonid..................................................................................................................................178 FH>?EVIEHKDHC<HEGU<KLHEDGH<BL?EVGHCD<:ABG?CLJ:EVGHCIE:AF?K=HJYQBFBWE?DLJHG:FBBOHEH>GUFBBHG:FB ?]hjh\Z?J ........................................................................................................................................179 G?EBG?CGHKLVLHEF?G:<L?HJBBD:IBEEYJGUOG:GH<HEG >he]bo:<.........................................................................................................................................181

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EHFHGHKH<– 2006

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<A:BFH>?CKL<B? IHEYJBAH<:GGUO WE?DLJHF:=GBLGUO <HEG K;B=BJHLJHIGHCE?<HCKJ?>HC B\Zgh\:< ........................................................................................................................................201 HILBFBA:PBY HILBQ?KDBO LJ:DLH< IJ?PBABHGGUO =:AH<UO:G:EBA:LHJH< Ahlh\:FLZgZq_\B: .................................................................................................................202 I:J:EE?EVGUC:E=HJBLFQBKE?GGH=H J?R?GBYG?KL:PBHG:JGHC A:>:QBHNBE:F?GL:PBBN?FLHK?DMG>GH=HE:A?JGH=HBFIMEVK: ;_a[hjh^h\:?..................................................................................................................................203 <UKHDHKL:;BEVGUC E:A?JGH-IE:AF?GGUC J?GL=?GH<KDBC BKLHQ-GBD KBKIHEVAH<:GB?FK<H;H>GHCIH<?JOGHKLB@B>DH=H=:EEBY **Dmjbeh\ZF<MjxibgZ>K ......................................................................................................206 HILBFBA:PBY <A:BFH>?CKL<BY L=P B HILBQ?KDH=H BFIMEVKH< <>BKI?J=BJMXS?CKJ?>? FZdZjh\ZK:GZaZjh\FF ..........................................................................................................208 BKKE?>H<:GB?F?LH>:E:A?JGH=HHL;?EB<:GBYKL:JBGGHC;MF:=B ;_ehrZidh\Z?:;jZg^lGGQbdbr_\:X ............................................................................210 WG?J=?LBQ?KDB?KI?DLJUIEHKDBO>?N?DLH<<'NHLHGGHFDJBKL:EE? R_gdZj_gdh:X ..............................................................................................................................211 HILBF:EVGU?MKEH<BY>EY<HA;M@>?GBYDBEV<:L?JGHC<HEGUE:A?JGUFBFIMEVKHF DZebggbdh\Z?B...............................................................................................................................212 E:A?JGUCFBDJHBGL?JN?JHF?LJ>EYBAF?J?GBCI:J:F?LJH<FBDJHLJM;HDB<HEHDHG EZaZj_\=E ........................................................................................................................................213 WE?DLJHF:=GBLGH-BG>MPBJH<:GGU? F:=GBLH-HILBQ?KDB? J?AHG:GKU <;?=MS?CWEEBILBQ?KDBIHEYJBAH<:GGHCK<?LH<HC<HEG? ;jZ`gbdh\>< ..................................................................................................................................215 KI?DLJHKDHIBQ?KDB?K<HCKL<:DJBKL:EEH<D:EVPBC-GBH;BC-=:EEB?<H=H=J:G:L::DLB<BJH<:GGH=HBHG:FB(r3+ FZeh\:<...........................................................................................................................................216 J?NJ:DLHF?LJG:HKGH<?IH<?JOGHKLGH=HIE:AFHGGH=HJ?AHG:G-K: K_j_]bgZGG .....................................................................................................................................217 :<LHGHFGUC IHABPBHGGH-QM<KL<BL?EVGUC >?L?DLHJ HILBQ?KDH=HBAEMQ?GBYG:HKGH<?IAK-F:LJBPU =Zebpbg<<......................................................................................................................................218 IHEMQ?GB?;B?GBC<HILBQ?KDHF>B:I:AHG?Q:KLHL >hfdbgDB........................................................................................................................................219 BAEMQ:L?EVGU? K<HCKL<: KEHBKLUO DJBKL:EEH< G-WS2 BGL?JD:-EBJH<:GGUOFHE?DME:FB=:EH=?GH< Dhe_\:B ..........................................................................................................................................220 THE PROBLEM OF FIELD CAUSALITY IN THE PROCESS OF SPONTANEOUS EMISSION OF TWO RADIATORS AT THE INITIAL STAGE OF EMISSION Galeamov E..........................................................................................................................................221 F?LH> >JH;GH=H <?C<E?L-IJ?H;J:AH<:GBY >EY H;J:;HLDB KI?DLJH<IH=EHS?GBY **;hg^Zj_\Z?:=Zebfmeebg>ANjheh\Z=<Kb[]ZlmeebgFWKZeZoh\FO ...............222

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