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Международная конференция студентов, аспирантов и молодых ...

Международная конференция студентов, аспирантов и молодых ...

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kbff_ljb_chlghkbl_evghhkb z H^gZdh_kebiheyjbaZpbyiheylZdh\ZqlhaZk_eyxlky<br />

ih^mjh\gb 1 P kjZagufbagZq_gbyfb M lh\k_q_gbbihy\ey_lkyaZ\bkbfhklvhlih<br />

eyjgh]h m]eZ Kl_i_gv iheyjghc Zkbff_ljbb aZ\bkbl hl iheyjbaZpbhgguo oZjZdl_jb<br />

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1. Mies F.H., Phys. Rev. 175 164 (1968).<br />

2. =_ee_jXB@WLN<br />

3. Heller Y.I., Phys. Lett. 82A 4 (1981).<br />

4. Bachau H., Phys. Rev. A 34 4785 (1986).<br />

5. Karapanagioti N.E., Phys. Rev. A 53 2587 (1996).<br />

6. Magunov A.I., Rotter I., Strakhova S.I. J. Phys. B: At. Mol. Opt. Phys., 32, 1669 (1999).<br />

7. Fano U., Phys. Rev 178 131 (1969).<br />

M>D<br />

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^bgZfbdb]b[_ebbhgh\O - ^Ze\hafh`ghklv\i_j\u_g_ihkj_^kl\_ggh\kZfhcieZaf_<br />

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− 3<br />

( O + O( P)<br />

→ O + e : k O d =(1.9±0.4)⋅10 -10 kf 3 k b fhe_dmeZo O 2 (a 1 û g )<br />

2<br />

−<br />

( O + O ( a<br />

1<br />

2<br />

∆<br />

g<br />

) → products + e : k ∆ d =(1.4±0.3)⋅10 -10 kf 3 k.<br />

Hkh[mxp_gghklvij_^klZ\ey_llhqlh\k_\_ebqbgug_h[oh^bfu_^eyhij_^_<br />

e_gby^ZgguodhgklZgl[uebihemq_guwdki_jbf_glZevghDjhf_lh]hwlb\_ebqbgu<br />

hljbpZl_evgu_bhguZlhfubkbg]e_lgu_fhe_dmeudbkehjh^Zbaf_jyebkv\©h^ghcª<br />

ijhkljZgkl\_gghc lhqd_ Wlh kms_kl\_ggh hlebqZ_l gZrb baf_j_gby hl ij_^u^msbo<br />

jZ[hl>@Ihwlhfmohl_ehkv[uihj_dhf_g^h\Zlvhij_^_e_ggu_\^ZgghcjZ[hl_dhg<br />

klZglukdhjhklb]b[_ebhljbpZl_evguobhgh\H – gZZlhfZoO( 3 Pbfhe_dmeZoO 2 (a 1 û g )<br />

^eybkihevah\Zgby\[ZaZo^Zgguo^eyfh^_ebjh\ZgbyieZafu<br />

[1] Lieberman M.A., Lichtenberg A.J. Principles of Plasma Discharges and Material Process<br />

ing. New York: Wiley, 1994.<br />

[2] Ramamurthi B., Economou D.J. // J. Vac. Sci. Technol. A, 2002, Vol.20, No. 2, pp. 467-<br />

478.<br />

[3] Panda S., Economou D.J. // J.Appl. Phys., 2000, Vol. 87, No. 12, pp. 8323-8333.<br />

[4] Fehsenfeld F.C., Albritton D.L., Burt J.A., Schiff H.I.// Can.J.Chem., 1969 Vol.47,<br />

p.1793.<br />

[5] Upschulte B.L., Marinelli W.J., Green B.D.// J.Phys.Chem., 1994, Vol.98, pp.837-842.<br />

GBFL:KL:;BEVGUOMJH


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AZibr_f\ujZ`_gb_^eydhgklZgluJηΣ 0 Σ 0 \\b^_<br />

g(ηΣ 0 Σ 0 ) = g ηuu F+g ηdd F+g ηss (F-D) = -g ηss D =√(2/3)D.<br />

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k\yabΣ 0 :<br />

√(1/2) m 2 η λ 2 Σ g(ηΣ 0 Σ 0 ) exp(-m 2 Σ /M 2 ) [1+A Σ M 2 ] =<br />

= m 2 η M 4 E0(x) [g ηss /12/π 2 /f η +3f 3η /4/f η /√(2)-M 2 /f η [g ηss [m d +<br />

m u ]- m 2 η /72/ f η [g ηss ]<br />

+ m 2 0 /6/ f η [ (g ηuu m d +g ηdd m u )] ≡ D(u,d,s)<br />

28


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pbZpbb CHF 3 we_dljhgguf m^Zjhf :[khexlgh_ agZq_gb_ ihegh]h k_q_gby ^bkkhpbZ<br />

pbbihemq_ghgZfbijbghjfbjh\d_gZwdki_jbf_glZevgu_^Zggu_ihbhgbaZpbhgghfm<br />

dhwnnbpb_glm\qbklhfCHF 3 :[khexlgh_agZq_gb_k_q_gby^bkkhpbZlb\gh]hijbeb<br />

iZgbywe_dljhgh\dfhe_dme_CHF 3 ihemq_ghbakjZ\g_gbyjZkq_lh\ijb\_^_ggh]hdh<br />

wnnbpb_glZbhgbaZpbbkwdki_jbf_glZevgufb^Zggufb<br />

GZhkgh\_ihemq_ggh]hohjhr_]hkh]eZkbyljZgkihjlguodhwnnbpb_glh\kwdk<br />

i_jbf_glZevgufb^ZggufbdZd\qbklhfCHF 3 lZdb\kf_kbCHF 3 :Arblh]h\ucgZ[hj<br />

k_q_gbcfh`_l[ulvbkihevah\Zgijbqbke_gghffh^_ebjh\Zgbbwe_dljhgghcdbg_lbdb<br />

\jZaebqguoieZaf_gguoj_ZdlhjZo<br />

1. Morgan L., Winstead C. and McKoy V. // J. Appl. Phys., 2001, v.90, p.2009<br />

2. Kushner M.J. and Da Zhang // J. Appl. Phys., 2000, v.88, p.3231<br />

3. Wang Y., Christophorou L.G. et al // Chem. Phys. Lett, 1999, v.304, p.303<br />

4. Christophorou I.G. Olthoff J.K. et al // J. Phys. Chem. Ref. Data, 1997, v.26, p.1<br />

5. Goto M., Nakamura K., Toyoda H. and Sugai H. // J. Appl. Phys., 1994, v.33, pp.3602-<br />

3607<br />

6. Phelps A.V., JILA Information Center Report N28, 1985<br />

31


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3. Borexino Collaboration «Science and technology of borexino: a real time detector for low<br />

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1. Fuller E.G., Gerstenberg H. Photonuclear Data - Abstracts Sheets 1955 - 1982. NBSIR<br />

83-2742. U.S.A. National Bureau of Standards, 1983.<br />

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3. Sergeev V.A., Sazhina E.M., Tsyganenko N.A. Pitch-angle scattering of energetic protons<br />

in the magnetotail current sheet as the dominant source of their isotropic precipitation into<br />

the nightside ionosphere // Planet Space Sci., 1983, vol. 31, 10, p. 1147-1155.<br />

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2. Hamai C., Tanaka H., and Kawai T. J. Vac. Sci. Technol. B 17, 1313.<br />

3. Gerritsen J.W., Elemans J.A.A.W., Hulsken B., Travaille A.M., Kempen H. van, Rasing<br />

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1. Sonnerup B.U.O. “Adiabatic particle orbits in magnetic null sheet” // J. Geophys. Res.,<br />

1971, v. 76, p. 8211.<br />

2. Chen J. and Palmadesso P.J. “Chaos and nonlinear dynamics of single-particle orbits in<br />

magnetotaillike magnetic field” // J. Geophys. Res, 1986, v. 91, p. 1499<br />

3. Hoshino M., Nishida A., Mukai T., Saito Y., and Yamamoto T. “Structure of plasma sheet<br />

in magnetotail: double-peaked electric current sheet” // J. Geophys.Res., 1996, v. 101 p.<br />

24775.<br />

4. Asano Y., Mukai T., Hoshino M., Saito Y., Hayakawa H., and Nagai T. “Evolution of the<br />

thin current sheet in a substorm observed by Geotail” // J. Geophys. Res.,2003, v. 108, p.<br />

10101.


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Ih^k_dpbyfZl_fZlbdb 105<br />

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Ih^k_dpbyfZl_fZlbdb 107<br />

4. Thual O., Frich U., Henon M. Application of pole decomposition to an equation governing<br />

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kebj_rZlvmjZ\g_gb_qbke_gghihy\ghcko_f_Jmg]_-DmllZlhqghklb Oτ ()<br />

ERK lh qbke_ggh_ j_r_gb_ [m^_l \k_]^Z iheh`bl_evguf b fhghlhggh \hajZklZx<br />

sbf<br />

2<br />

u = u( 0 ); u = u+τ u , n= 0,1,...; tn<br />

= nτ (3)<br />

0<br />

ˆ<br />

Ijbwlhfgbqlhg_]h\hjblh[hkh[_gghklbj_r_gby\lhqd_ t *<br />

bkoh^yba\b^Z<br />

fh`ghk^_eZlv\u\h^qlhj_r_gb_kms_kl\m_lijbex[uo t n<br />

GZijZdlbd_ijbf_<br />

g_gb_ko_fuijb t →∞ijb\h^bldi_j_iheg_gbxkq_lZZijbqbgZi_j_iheg_gby<br />

hklZzlky g_ba\_klghc :gZeh]bqgh_ dZq_kl\_ggh_ ih\_^_gb_ qbke_ggh]h j_r_gby ^ey<br />

aZ^Zqkkbg]meyjghklvxoZjZdl_jgh^eyko_fERKb[he__\ukhdh]hihjy^dZlhqghklb<br />

@dhlhjuc<br />

iha\hey_l ^bZ]ghklbjh\Zlv g_ lhevdh iheh`_gb_ gh b lbi hkh[_gghklb j_r_gby <<br />

kemqZ_kl_i_gghchkh[_gghklb\b^Zfh`ghmklZgh\blvihjy^hdihexkZ β Ihkljh_<br />

gZlZd`_^bZ]ghklbdZjZaju\h\\ukhdboijhba\h^guolhqgh]hj_r_gby:\lhjZfbih<br />

dZaZghqlhijbf_g_gb_ko_fuCROSbagZqZevghij_^eh`_gghc^ey`_kldboaZ^Zqg_<br />

ijb\h^bldi_j_iheg_gbxjZkq_lh\biehohh[mkeh\e_gguoaZ^Zq<br />

H^ghiZjZf_ljbq_kdh_ k_f_ckl\h h^ghklZ^bcguo ko_f Jha_g[jhdZ ^ey mjZ\g_<br />

gby<br />

u′ t = F u,<br />

t<br />

() ( )<br />

hibku\Z_lkyke_^mxsbfnhjfmeZfb<br />

u = u 0 ; u = u+τRe k; E−ατ∂F ∂ u k = F u, t+ 0.5τ . (4)<br />

( ) ( ) ( )<br />

0<br />

ˆ<br />

** >hdeZ^hlf_q_g`xjbdZdh^bgbaemqrbogZih^k_dpbb


108<br />

EHFHGHKHeyi_j_oh^ZgZke_^mxsbc\j_f_gghckehclj_[m_lkyj_rblvkbkl_fmebg_cguoZe<br />

]_[jZbq_kdbo mjZ\g_gbc k fZljbp_c ( E−ατ∂F ∂u)<br />

Lh _klv i_j_oh^ gZ gh\uc kehc<br />

dZdb\y\guo ko_fZoijhbkoh^blaZdhg_qgh_aZjZg__ba\_klgh_qbkehrZ]h\LZdb_<br />

ko_fu gZau\Zxlky y\gh-g_y\gufb Kms_kl\m_l h^gZ ko_fZ CROS ba k_f_ckl\Zk<br />

2<br />

dhfie_dkgufiZjZf_ljhf α= ( 1+ i)<br />

2mgbdZevgufbk\hckl\Zfblhqghklv<br />

O( τ ), L2-<br />

mklhcqb\hklv fhghlhgghklvxgZebg_cguoaZ^ZqZobbkdexqbl_evgZygZ^_`ghklvgZ<br />

`_kldboaZ^ZqZo<br />

Dhgljhev lhqghklb f_lh^hf k]ms_gby k_ldb ij_^eh`_g _s_ JbqZj^khghf \<br />

1927 ]Kmlvf_lh^ZaZdexqZ_lky\lhfqlhihj_amevlZlZfjZkqzlh\gZ^\mok_ldZok<br />

N b rN maeZfbih]j_rghklvqbke_ggh]hj_r_gby\kh\iZ^ZxsbomaeZok_lhd\uqbk<br />

ey_lkyihZkbfilhlbq_kdblhqghcijb N →∞nhjfme_<br />

( rN ) ( N )<br />

( rN ) u −u<br />

−p<br />

∆ () t = + o<br />

p ( N )<br />

(5)<br />

r −1<br />

]^_p –l_hj_lbq_kdbcihjy^hdlhqghklbko_fu<br />

2<br />

Ihj_amevlZlZfjZkqzlh\gZljzok_ldZoNrNrNfh`gh\uqbkeblvwnn_d<br />

, ,<br />

lb\gucihjy^hdlhqghklbko_fu<br />

( N) ( rN)<br />

eff ln ∆ −ln<br />

∆<br />

p () t = .<br />

(6)<br />

ln r<br />

F_lh^bdZ ^bZ]ghklbdb kbg]meyjghklb gZ hkgh\_ f_lh^Z k]ms_gby k_ldb b ijb<br />

jZkq_lZoko_fhcCROS[Zabjm_lkygZke_^mxsbo^hdZaZgguoZ\lhjZfbml\_j`^_gbyo<br />

Ml\_j`^_gb_ 1. Kms_kl\m_l agZq_gb_ u = ⎡<br />

β<br />

∗ ⎣2 τ ( β+ 1)<br />

⎤ ⎦ , ijbdhlhjhfqbke_ggh_<br />

j_r_gb_ko_fu&526^eyaZ^Zqbg_f_gy_lkyijbi_j_oh^_gZke_^mxsbc\j_f_g<br />

ghckehc û : û = u ∗<br />

.<br />

Ml\_j`^_gb_ k\hckl\h ijbly`_gby. Ijb u > u ∗<br />

ijbjZs_gb_ nmgdpbb<br />

uˆ − u < 0 bgZh[hjhlijb u < u ∗<br />

ijbjZs_gb_nmgdpbb uˆ − u > 0 . L_ijbex[hfagZq_<br />

gbb u gZl_dms_f\j_f_gghfkeh_ke_^mxsbcrZ]ko_fZ&526^_eZ_lihgZijZ\e_<br />

gbxdiheh`_gbxjZ\gh\_kby u = ⎡<br />

β<br />

∗ ⎣2 τ ( β+ 1)<br />

⎤ ⎦ .<br />

Ml\_j`^_gb_ Ijbhkh[_gghklblhqgh]hj_r_gbyH>MlbiZihexkZ β> 0<br />

qbke_ggh_ j_r_gb_ ko_fu CROS klj_fblky dij_^_em u ∗<br />

. Ijbhkh[_gghklblbiZdhjgy<br />

−1≤β< 0 qbke_ggh_j_r_gb_ko_fu&526klZ[bebabjm_lky\ihehk_\hdjm]iheh`_<br />

gbyjZ\gh\_kby u ∗<br />

.<br />

>eyH>Mlhqgh_j_r_gb_dhlhjh]hbf__lhkh[_gghklv\b^Z u ln( t t)<br />

∗− kijZ<br />

\_^eb\uml\_j`^_gby<br />

Ml\_j`^_gb_ Kms_kl\m_liheh`_gb_jZ\gh\_kby u ∗<br />

= ln τ− ln 2 , ijbdhlhjhf<br />

qbke_ggh_j_r_gb_ko_fu&526g_f_gy_lkyijbi_j_oh^_gZke_^mxsbc\j_f_gghc<br />

kehc<br />

Ml\_j`^_gb_ 5. Ijb u > u ∗<br />

ijbjZs_gb_ nmgdpbb uˆ − u < 0 b gZh[hjhl ijb<br />

u< u ∗<br />

ijbjZs_gb_nmgdpbb uˆ − u > 0 .<br />

Ml\_j`^_gb_ 6.


Ih^k_dpbyfZl_fZlbdb 109<br />

Ml\_j`^_gby iha\heyxlmklZgh\blvihjy^hd β ijbkl_i_gghchkh[_gghklb<br />

() ( − ) beb^bZ]ghklbjh\Zlveh]Zjbnfbq_kdmxhkh[_gghklv u() t ln ( t t)<br />

u t t*<br />

t −β<br />

*<br />

− .<br />

Ml\_j`^_gb_ Ijb gZebqbb kbg]meyjghklb lhqgh]h j_r_gby lbiZ<br />

u() t ( t*<br />

− t)<br />

−β<br />

eff<br />

\ maeZo t ≥ t*<br />

wnn_dlb\guc ihjy^hd lhqghklb ko_fu &526 p →−β<br />

1<br />

ijb τ N − → 0 .<br />

Ml\_j`^_gb_ Ijb gZebqbb kbg]meyjghklb lhqgh]h j_r_gby lbiZ<br />

u() t ln ( t*<br />

− t)<br />

\maeZo t ≥ t*<br />

ih]j_rghklv ko_fu CROS ( N ) ln r<br />

−p<br />

∆ () t =− + o<br />

p ( N ), Z<br />

r −1<br />

eff<br />

1<br />

p → 0 ijb τ N − → 0 .<br />

;ueb ijh\_^_gu fgh]hqbke_ggu_ l_klh\u_ jZkq_lu k jZaebqguf lbiZfb hkh<br />

[_gghkl_clhqgh]hj_r_gbyEBJH:JGHCHFKLJEV;U<br />

Ohoeh\::<br />

F=MbfF@<br />

F_lh^qbke_ggh]hj_r_gbymjZ\g_gbcGKaZdexqZeky\ke_^mxs_f–^eyklZ<br />

pbhgZjghc aZ^Zqb mjZ\g_gby \lhjh]h ihjy^dZ ih ijhkljZgkl\m bgl_]jbjh\Zebkvh^bg


110<br />

EHFHGHKHZggu_ j_amevlZlu ^_fhgkljbjmxl qlhlhqghklv mjZ\g_gbcGZ\v_-KlhdkZ ^ey<br />

aZ^ZqbhibkZgbykljmdlmjum^Zjghc\hegukms_kl\_ggh\ur_q_fkqblZehkvjZg__<br />

1. Dh]ZgFG>bgZfbdZjZaj_`_ggh]h]ZaZF<br />

2. ebaZjh\Z L= Rbjhdh\ B: Qbke_ggh_ fh^_ebjh\Zgb_ m^Zjghc \hegu \<br />

Zj]hg_ ]_ebb b Zahl_ K[ IjbdeZ^gZy l_fZlbdZ b bgnhjfZlbdZ j_^<br />

>IDhklhfZjh\ fbljb_\ F=M Ljm^u nZdmevl_lZ


Ih^k_dpbyfZl_fZlbdb 111<br />

M>D<br />

H;JHLGHKLB<br />

KNJBQKDB-KEHBKLH=H>BWEDLJBQKDH=HJAHG:LHJ:<br />

∗ =msbgJ:jhobg:B<br />

F=MbfF@Ihemq_gb_j_r_gby^eyj_ahgZlhjh\[he__keh`guodhgkl<br />

jmdpbclj_[m_lbkihevah\Zgbyqbke_gguof_lh^h\@bkke_^h\Zekykn_jbq_<br />

kdbc j_ahgZlhj k bfi_^Zgkghc [hdh\hc ih\_joghklvx ^bnn_j_gpbZevghiZjZf_ljbq_kdbff_lh^hf@qbke_gghbkke_^h\Zebkv\ukhdh^h[jhlgu_dhe_[Zgby<br />

lbiZ r_iqms_c]Ze_j_b\wdjZgbjh\Zgghfkn_jbq_kdhf^bwe_dljbq_kdhfj_ahgZlhj_<br />

Kh[kl\_ggu_ dhe_[Zgby kn_jbq_kdb-kehbklh]h j_ahgZlhjZ k bfi_^Zgkghc ih\_jogh<br />

klvxjZkkfZljb\Zebkv\>@<br />

GZklhysZy jZ[hlZ ihk\ys_gZ \uqbke_gbx ^h[jhlghklb kn_jbq_kdb-kehbklh]h<br />

^bwe_dljbq_kdh]h j_ahgZlhjZ k bfi_^Zgkghc ih\_joghklvx Dhfie_dkgu_ \hegh\u_<br />

qbkeZgZoh^bebkvijbqbke_gghfj_r_gbboZjZdl_jbklbq_kdh]hmjZ\g_gbyaZibkZggh<br />

]h\\b^_jZ\_gkl\Zgmexhij_^_ebl_eykh^_j`Zs_]hkn_jbq_kdb_nmgdpbb;_kk_ey<br />

bjh^Zbboijhba\h^gu_>eywlh]hijbf_gyeky[bgZjgucbl_jZpbhggucdhjj_dlhjijhp_kk>@hkgh\ZggucgZijh^he`_gbbj_r_gbyf_lh^hf^bnn_j_gpbjh\ZgbyihiZ<br />

jZf_ljmkmlhqg_gb_fj_r_gbyf_lh^hfGvxlhgZ<br />

;ueh bkke_^h\Zgh \ebygb_ gZ ^h[jhlghklv j_ahgZlhjZ ]_hf_ljbq_kdbo b we_d<br />

ljh^bgZfbq_kdbo iZjZf_ljh\ jZkiheh`_gby bfi_^Zgkgh]h wdjZgZ jZ^bmkZ rZjh\h]h<br />

^bwe_dljbq_kdh]haZiheg_gby\u[hjZlbiZdhe_[Zgbcb^jm]bonZdlhjh\H[gZjm`_gh<br />

qlhijbm^Ze_gbbwdjZgZ^h[jhlghklvj_adh\hajZklZ_lZihlhfklZ[bebabjm_lkyIjb<br />

hij_^_e_gguo we_dljh^bgZfbq_kdbo iZjZf_ljZo aZiheg_gby kms_kl\m_l hilbfZevgh_<br />

jZkiheh`_gb_bfi_^Zgkgh]hwdjZgZijbdhlhjhf^h[jhlghklvfZdkbfZevgZIjb\ha<br />

jZklZgbb ZabfmlZevgh]h b jZ^bZevgh]h bg^_dkh\ gZ[ex^Z_lky \hajZklZgb_ ^h[jhlgh<br />

klb<br />

1. Bevbgkdbc:KKe_iyg=YDhe_[Zgbyb\hegu\we_dljh^bgZfbq_kdbokbkl_fZok<br />

ihl_jyfb–FBa^-\hFhkdmg-lZ<br />

2. Fh^_gh\


112<br />

EHFHGHKH


Ih^k_dpbyfZl_fZlbdb 113<br />

M>D<br />

JRGBMJ:ey ij_^eh`_ggh]h Ze]h<br />

jblfZijh\_^_ghihegh_l_hj_lbq_kdh_h[hkgh\Zgb_>hdZaZgul_hj_fukms_kl\h\Zgby<br />

b_^bgkl\_gghklbZlZd`_koh^bfhklvijb[eb`_ggh]hj_r_gbymk_q_gghckbkl_fud<br />

lhqghfm<br />

Ijb j_r_gbb djZ_\hc aZ^Zqb \ fgh]hk\yaghc \hegh\h^ghc h[eZklb k dmkhqgh-<br />

]eZ^dhc ]jZgbp_c Ze]hjblf ihkljh_gby ijb[eb`_ggh]h j_r_gby [ue hkgh\Zg gZ bk<br />

ihevah\Zgbbg_ihegh]hf_lh^Z=Ze_jdbgZ>@kijbf_g_gb_fbgl_]jZevguomkeh\bc<br />

ijh_dpbhggh]hkrb\ZgbyKmlvijb[eb`_ggh]hf_lh^Zj_r_gbyaZdexqZ_lky\nhjfm<br />

ebjh\d_kbkl_fumkeh\bchjlh]hgZevghklbh[_ki_qb\Zxs_c\uiheg_gb_\wg_j]_lbq_<br />

kdhfkfuke_mkeh\bckrb\Zgby\iehkdhklbkhqe_g_gby\hegh\h^h\b]jZgbqguomk<br />

eh\bcgZkl_gdZoIj_^klZ\e_gb_^eyijb[eb`_ggh]hj_r_gby\h[eZklbg_j_]meyjgh<br />

klb\u[bjZehkvihkbkl_f_nmgdpbcg_aZ\bkysbohlnhjfu\hegh\h^Z>eywlh]h[u<br />

ehijh\_^_ghhlh[jZ`_gb_\gmlj_gg_ch[eZklb\hegh\h^Zkg_j_]meyjghklvxgZj_]m<br />

eyjgmx ihehkm < blh]_ djZ_\Zy aZ^ZqZ ^ey mjZ\g_gby \ qZklguo ijhba\h^guo [ueZ<br />

k\_^_gZ d djZ_\hc aZ^Zq_ ^ey kbkl_fu h[udgh\_gguo ^bnn_j_gpbZevguo mjZ\g_gbc


114<br />

EHFHGHKHeyjZkkfZljb\Z_fh]hZe]hjblfZlZd`_^hdZaZgul_hj_fu<br />

kms_kl\h\Zgby_^bgkl\_gghklbbkoh^bfhklvijb[eb`_ggh]hj_r_gbydlhqghfm<br />

>eyj_r_gbydjZ_\hcaZ^Zqb\fgh]hk\yaghch[eZklbkih\lhjyxs_ckyg_j_]m<br />

eyjghklvx ijbf_gyeZkv dhf[bgZpby ijh_dpbhggh]h f_lh^Z krb\Zgby >@bf_lh^Z<br />

fgh]hfh^h\uofZljbpjZkk_ygbyS-fZljbp>@F_lh^hf^_dhfihabpbbkbkl_fZjZa<br />

[b\ZeZkvgZk_jbxb^_glbqguowe_f_glZjguo[ehdh\S-fZljbpZwe_f_glZjgh]h[ehdZ<br />

jZkkqblu\ZeZkv ijh_dpbhgguf f_lh^hf krb\Zgby b ^Ze__ k bkihevah\Zgb_f nhjfme<br />

i_j_fgh`_gbyS-fZljbpjZkkqblu\ZeZkv\kykljmdlmjZ<br />

>ey jZkkfhlj_gguo Ze]hjblfh\ [ueZ ijh\_^_gZ qbke_ggZy j_ZebaZpby Ihem<br />

q_ggu_ j_amevlZlu kjZ\gb\Zebkv k nbabq_kdbf wdki_jbf_glhf>@bj_amevlZlZfb<br />

^jm]bo\uqbkebl_evguof_lh^h\>@<br />

< j_amevlZl_ ih^]hlh\e_g wnn_dlb\guc fZl_fZlbq_kdbc ZiiZjZl bf_xsbc<br />

\hafh`ghklbh[h[s_gbygZlj_of_jgu_b\gmlj_gg_-\g_rgb_aZ^Zqb<br />

1. KZahgh\>F=jb^bg:GFbrmklbg;:Mkljhckl\ZK


Ih^k_dpbyfZl_fZlbdb 115<br />

k]jZgbqgufbmkeh\byfbG_cfZgZgZ]jZgbpZoihehku ∂ Ω= { y =0 , y = 1}<br />

:<br />

∂u<br />

= 0<br />

∂n<br />

∂Ω<br />

(2)<br />

bmkeh\bx<br />

u ∈ L 2(<br />

Ω )<br />

(3)<br />

J_r_gb_ mjZ\g_gbym^h\e_l\hjyxs__ ]jZgbqguf mkeh\byfbmkeh\bx<br />

[m^_fgZau\Zlveh\mr_qghcfh^hc<br />

Ij_^iheZ]Z_lkyqlh<br />

q( x,<br />

y)<br />

≡ 1<br />

ijb x < x , x > x 1 2 b<br />

q( x,<br />

y)<br />

> 1<br />

ijb<br />

x<br />

1<br />

< x < x2<br />

GZ<br />

⎡∂u⎤<br />

[] u = 0 ,<br />

⎢ ⎥<br />

= 0<br />

σi<br />

⎣∂n⎦<br />

σ σ<br />

i<br />

ebgbyojZaju\Z\uihegyxlkymkeh\bykhijy`_gby<br />

]^_<br />

i -ebgby<br />

2<br />

2<br />

∇u<br />

+ u < ∞<br />

L ( Ω ) ( Ω )<br />

jZaju\Z\dZq_kl\_mkeh\by©gZj_[j_ªihlj_[m_fqlh[u<br />

2 ε L2<br />

ε<br />

]^_<br />

Ωε<br />

-ex[Zydhg_qgZyih^h[eZklvh[eZklb Ω \lhfqbke_kh^_j`ZxsZym]eh\mxlhqdm<br />

[1].<br />

>eyqbke_ggh]hbkke_^h\ZgbyjZkkfZljb\Z_fhcaZ^Zqbm^h[ghi_j_clbhlaZ^Z<br />

qb\[_kdhg_qghch[eZklbdaZ^Zq_\dhg_qghckg_ehdZevgufbdjZ_\ufbmkeh\byfb<<br />

j_amevlZl_i_j_c^_fd\gmlj_gg_cdjZ_\hcaZ^Zq_wd\b\Ze_glghcaZ^Zq_-(3)<br />

∂u<br />

∂x<br />

∂u<br />

∂x<br />

x=<br />

x<br />

x=<br />

x<br />

∂u<br />

∂n<br />

2<br />

− ∆u = k q(<br />

x,<br />

y)<br />

u<br />

(4)<br />

∂u<br />

= 0,<br />

∂n<br />

y= 0<br />

y= 1<br />

∑ ∞<br />

= 1<br />

= 0<br />

= 2 γ<br />

n<br />

( u,cos(<br />

πny))<br />

2 1<br />

1<br />

n<br />

∑ ∞<br />

= 1<br />

= −2 γ<br />

n<br />

( u,<br />

cos( πny))<br />

2 2<br />

2<br />

n<br />

( u,1)<br />

L 2(<br />

S i<br />

)<br />

= 0, i = 1, 2<br />

L ( S )<br />

cos( πny)<br />

L ( S )<br />

cos( πny)<br />

Ijbwlhfki_dljZevguciZjZf_lj\oh^blg_ebg_cguch[jZahf\djZ_\u_mkeh\byq_j_a<br />

γ<br />

dhwnnbpb_glu n<br />

(k)<br />


116<br />

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kg_kbff_ljbqghchlghkbl_evghhkb^bwe_dljbq_kdhc\klZ\dhc<br />

Hkgh\gu_\hijhkubkke_^h\ZgbyaZdexqZebkv\ke_^mxs_f<br />

—khojZgy_lkyebmkeh\b_ ( u ,1) = 0^ey\hegh\h^Zkg_kbff_ljbqghchlgh<br />

L2 ( S i )<br />

kbl_evghhkb^bwe_dljbq_kdhc\klZ\dhc"<br />

—DZdh\hih\_^_gb_maeh\hcebgbb"<br />

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l_evghhkbEbgbbmjh\gyj_r_gbyaZ^Zqb-bf_xl\b^<br />

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Ih^k_dpbyhilbdb 143<br />

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Ih^k_dpbyhilbdb 149<br />

4. Plihal M., Shambrook A., Maradudin A.A. “Two-dimensional photonic band structures”,<br />

Optics Communications, vol. 80, No. 3, 1 January 1991.<br />

M>D-14<br />

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Ih^k_dpbyhilbdb 151<br />

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4. Iskhakov T.Sh., Ivanova O.A. and Chekhova M.V. "Multi-photon states and their measurement"<br />

// Proceedings of the Second International Symposium Quantum Informatics,<br />

October 5-8 2004, Moscow, Proceedings of SPIE, 2005.<br />

5. Brown R., Hanbury R.Q. and Twiss R.Q., 1964, Nature, London, 177, 27.<br />

6. Haner A.B. and Isenor N.R. "Intensity Correlations from Pseudothermal Light Sources" //<br />

American Journal of Physics, June 1970, volume 38, number 6, p. 748-751.<br />

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Ih^k_dpbyhilbdb 153<br />

6<br />

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1. Kivshar Y.S., Ostrovskaya E.A. // Optics&Photonics News. 2002. V. 2. P. 28.<br />

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Andre Y.-B., Mysyrowicz A., Souerbrey R.., Wolf J.-P., Wöste L. Science. 2003. Vol.<br />

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Super-Gaussian Output in a CW-CO2 Laser. IEEE Journal Of Quantum Electronics<br />

Vol.30, No.11, November 1994<br />

2. Cherezova T., Chesnokov S., Kaptsov L. Kudryashov A. Super-Gaussian laser intensity<br />

output formation by means of adaptive optics. Optics Communications 155 (1998) 99 –<br />

106.<br />

3. Fox A., Li T. Effect of Gain Saturation on the Oscillating Modes of Optical Masers. IEEE<br />

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4. Sheldakova J., Rukosuev A.L., Kudryashov A.V. Genetic and hill-climbing algorithms for<br />

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1. Handbook of Optical Coherence Tomography, Bouma B.E., Tearney G.J., eds. (New<br />

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1. Kaesarmann F., Kempf Ch. Buckminsterfullerene and Photodynamic Inactivation of Viruses.<br />

Reviews in Medical Virology 1998, 8, 143-151


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2. Da Ros T., Spallutto G., Prato M. Biological Applications of Fullerene Derivatives:A<br />

Brief Overview. Croatical Chemica Acta. 2001, 74 (4), 743-755<br />

3. Scharff P., Risch K., Carta-Abelmann L., Dmytruk I., Bilyi M., Golub O., Khavryuchenko<br />

A., Buzaneva E., Aksenov V., Avdeev M., Prylutskyy Yu., Durov S. Structure of C 60<br />

fullerene in water: spectroscopic data. Carbon, 2004, 42(5-6), 1203-1206<br />

4. Heymann D., Bachilo S., Weisman B., Cataldo F., Fokkens R., Nibbering N., Vis R., Chibante<br />

F.. C 60 O 3 , a Fullerene Ozonide: Synthesis and Dissociation to C 60 O and O 2 .<br />

J.Am.Chem.Soc. 2000, 122, 11473-11479<br />

5. Richard D. Webster and Graham A. Heath, Voltammetric, EPR and UV-VIS-NIR spectroscopic<br />

studies associated with the one-electron oxidation of and in C 60 C 70 1, 1’, 2, 2’-<br />

tetrachloroethane containing tri-uoromethanesulfonic acid, Phys. Chem. Chem. Phys.,<br />

2001, 3, 2588 – 2594


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