NUMERICAL MODELLING SUBSONIC AND SUPERSONIC INDUCTIVE PLASMA FLOWS

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1 o Cogss o Cotto Mtods Ad Sccs d gg CCOMAS Cotto Fd Dcs Cofc Sws Ws UK 4-7 Stb CCOMAS NUMRICAL MODLLING SUBSONIC AND SUPRSONIC INDUCTI PLASMA FLOWS Sg. Utzko * Ad.Koko* Ds.Rdko* Sg A. s'sk** Ato F. Kosko** d G.S.R. S*** Dtt of Mcc gg UMIST P.O. Bo 88 Mcst M6 QD UK -: s.tzko@st.c.k * Moscow Isttt of Pscs d Tcoog Dogod 47 Rss ** Isttt fo Pobs Mccs RAS Posct dskogo Moscow *** DLR Isttt f Stogsck Bs st. D-3773 Gottg G K wods: Psto N-Stoks qtos ow Mc b fows g tts TD scs. Abstct. A sco-cc od c tod d cotto sts fo qb dct cod s fows sto std. Nc sotos of t N-Stoks qtos cod wt qs-d oto of t Mw qtos fo stto stc fows wt swg b obtd. A w ffct codtog tcq og wt ct TD sc s sd to so t N-Stoks qtos bot sbsoc d ssoc gs. To st t fow t f N-Stoks qtos wtt t cdc coodt sst wt ccot fo t oct coots - d d tgt coot d to t fow sg togt wt g qto wtt fo t tot gs t. T qtos cd soc ts cosodg to t ctogtc fd fc: t Lotz foc coots so cd gtc ss d Jo t odcto. T css tsot coffcts w cctd dc fo qb s s t fctos of ss d tt. Tsot ots w cctd b t cs fo of t C-skog tod tt g 3 T 5 K fo f gss: tog og go cbo dod. Cctos of qb tog og go d cbo dod s fows fo t IPG-4 IPM Moscow dscg c got wt t c ds Rc.4 d gt Zc.46 w fod. Two cods w dod to c ot t cctos. T fst cod cod s bsd o t SIMPL got wt t d-to ocd fo og stbt. T t-to tod og wt t ct sc d codtog s sd t scod cod cod.

2 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S INTRODUCTION A od cto of t dct cod ss s stg tocc tcto of g-t gs fows wt t otcto ts TPM t t soc fgt codtos -4. T IPG stos t IPM RAS d to b ffct toos fo t TPM ot tstg d t dcto of t TPM ctct. T ffct cbts of t -kw IPG-4 sto fo t sto of sco-cc ocsss ccog t soc t of c os t Mt tos b dosttd ct 56. Bt fct t ott cbts of R&D fcts to st ctg fow scs d sfc ocsss c b d f t sts o cobd wt CFD odg. CFD odg s dssb too fo ot tstg od to c ot CFD cods dto to bd fow fd sto d to tct TPM ctct td to tos cobto fo t tsf sts. I g t ob s t tck. U to ow t fw cottos of t oqb s fow cod wt t RF ctogtc fd 7. T oso of CFD odg dod t IPM cossts t sto of t wo fow fd to sto t cotto zos w t dstct fow fts c b sd fo t ffct oc 6. Fo t sto otg codtos t g CFD ob s ddd t t obs s foows:. t qb dct cod swg s fow wt t cdc dscg c;. t qb sbsoc stc g-t jt fow st cdc od; 3. t oqb tcoot bod wt t ft tckss t t stgto ot. A w c got std d cot cod b dod to st t ob wtot ddg do to dfft sbgos. T got ows s to st bot sb- d ssoc gs q. I t w st t cbts of CFD odg dct cod ss d so sts of cottos cd ot b two dfft cods t wd g of t IPG-4 sto otg codtos fo dfft qb ss tog og cbo dod go. T dcd tcoog dod fo cctos of t s tsot coffcts bsd o t goos odfcto of t C-skog fos 8 d ot dtbs fo todc d tsot ots std s w. Two cods w sd to c ot t cctos. T fst cod s bsd o t SIMPL got wt t d-to ocd fo og stbt. T t-to tod og wt t ct sc d codtog s sd t scod cod. A coso of bot cods ws do 9. A w oc ow to s codtog tcqs wt TD scs s sggstd. I t sc cs of t Ro sc t tod s obtd. I t tcts of t s of wd scs t ow Mc bs w cosdd fo t fst t w t ws sow ow t codtog tcq c t obs cocd wt oosg ccc t ow Mc bs.

3 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S 3 GORNING QUATIONS Ps fow dcto sto dscg c d t LT codtos s ssd to b god b t N-Stoks qtos fo cossb gs tkg to ccot t Lotz foc d Jo tg d t Mw qtos fo RF ctogtc fd. T gs dc sbst of gog qtos wt t Jo t soc of t ctc sstc d wt t Lotz foc t s s foows: z t S S S - G G - U. w U w w G w w S J Q F S µ z z z zz z z zz P w z z P w µ G z z w P µ S µ 3 z zz µ 3 z z µ 3 µ z z µ w w z w z µ w T qtos wtt cdc coodts z z cosods to t

4 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S coodt - d. A st wt o zo tss ot s ssd. Id cosods to scd f ctos d soc ts d cosods to t scos os. T coot of t Lotz foc s gctd. T gd Lotz foc d Jo tg t t gt d sd of. ssd t ts of t ctc fd wc s ssd to b t s of two cotbtos P w s dcd b ct t dcto co w P s gtd b otc cts s. s cctd b s of t Bot-St w oc bfo sog.. T s-dcd ctc fd td P s god b Uk P z P P πµ σf P t s-dcd ctc fd. P s dtd t c tto o t st. T gog qtos cosd wt costtt tos wc df ctc codctt tsot ots d qto of stt of s d LT codtos. T qto of stt codctt d tsot ots dd tb fo. 3 NUMRICAL APPROIMATION OF TH HYPRBOLIC PART OF TH GORNING QUATIONS BY IMPLICIT TD SCHM A stctd gd wc s dt to t fow got s sd. A tc foto s ssd t ts of ft o tod ottos. T scod od wd TD sc og dod b Ht d Y s sd to ot f ctos d f cto Jcob tcs t t c fcs. T sc s bsd o oc cctstc oc d s t scod od of ccc sc ost w ctg t of t cctstc bs. T cosodg st of gbc qtos c b wtt δ-fo s I F A o < k 4 < F F > o k 4 k U > k o S S o U S S S U U w d k dtfs o of c fcs {-/ j; / j; j-/; j/} bckts T < f > k dot c oto of fcto f t fc k U s t T cto of t cost bs U U - U o s t o of c H T F G s cto of scos fs s t o F G cto to c fc s oto stg fo zto 3. 4

5 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S of t scos fs. Nc scd f cto t fc / j s g b > / j F / j U j F / j U / j Φ < F j R / j T t R / j sts t gt gctos of t Jcob t A U cosodg to t f cto F U. T ts φ of cto Φ fo t wd TD sc t scod d j s ottd w fo sct: φ / ψ / g g ψ / γ / α / 3. w / t gs of t Jcob t A U α/ s ots to of t oc cctstc bs t dots α / R / U U. γ / g od α/ α / g g α / ψ / α / α / T coffct of c scost coctd to stsf to qt s g b t fo z z ε ψ z z ε z < ε ε A > / j T oto of t c f Jcob t t c fc /j < s obtd ft zto of t c f t g b 3. w < A > / j U j Ω A / j / j U U j j U - U j j A / j Ω / j R / j dg[β ψ γ ] / j R β / j g j g j α / j U j / j U j 5

6 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S 6 s j / j R / / j R cctd b gg ocd of so kd. Sc qto of stt fo ctg gs s sd t cottos of s fow sd sto toc tc fo of t fctos of stt sod b sd. T Jcob tcs d t tcs of ft d gt gctos fo t cs of bt qto of stt g bow. T f cto stg fs of cost bs U tog t c fc s F F cosodg Jcob t s A w k k U c b ssd ts of s foows 3 4 T gsst dcoosto of Jcob t s t fo R dg R A ] [ σ σ s t sod oct σ s t of t fc. Mtcs of t gt d t ft gctos g b α α α α α α α α R Φ Θ Φ Θ Θ β β β βφ β β β βφ φ R

7 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S 7 w σ σ t coots of t t o α β Θ.5 φ Φ P P P P P 3. Pcodtog gog qto sst T gs fow sd sto dscg c s cctzd b ow Mc b s. < M <. As w kow t gog qtos bco stff s Mc b tds to zo d ts t cogc t of t tto ocd s sow. I ct s b of codtog tods b dod b s tos to so t ob. T codtog t s t sst dgo fo ] [ β dg P t bs ss - to T S W. H β s codtog t. T t codtog t cost bs T U s s foows U W W U U W W U P P P c 3.3 O c obt c of t codtog t cost bs fo gs wt bt qto of stt φ φ φ φ β I P c w I s t t t d φ

8 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S Istd of 3. w so S S P F 3.4 c A k o o < > U k 4 U U U < F F > k o S S S o k 4 Bt TD oto s costctd 3.4 s fo t sst So tt U - G -G c P t z S S S < F > / j F / j U j F / j U j P c / j R / j Φ < A > / j Uj A / j U j U j A / j U j U P Ω U - U / j φ c / j / j j j ψ / j g j g j ψ / j γ / j α [β ] Ω R dg ψ γ R j / / j / j / j / j j / j w R d cosod to t gt gctos t d gs of t t P c A ccodg. It s s to sow tt foowg ts w t s ossb to ddc t tod obtd fo t Ro sc of t fst od of oto. A ot fctozto tod s d to so 3.4 Pc L L j U RHS w L L j t otos t ft d sd of 3.4 cosodg to dfft coodt dctos. A ot fctozto s s foows P L P P L U RHS 3.5 c j c c Ts t soto ocd t c tto o t st cossts of s sts 8

9 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S P L U / RHS 3.6 P U c c L j U U U P c U / Nc tsts w cd ot dtc ot cogc t odd codto 3.3 s sd. Tst std stt cctos fod fo scos fow cs wt dbtc ws. Rsts sow Fg. d cosod to M o - w M o -s Mc b t t t of t c. T b of ttos qd to ds t o of t sd to -6 s sow gst CFL b fo bot t codtod d o codtod tods. I Fg. t oto of t sd o t t g CFL b s std. Fg.: Nb of ttos qd to ds t o of t sd to -6 Fg.: oto of t o of sd fo dfft s of t codtog t 9

10 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S It sod b otd tt ts sts f to t cs w t s o t tg. If t stog tos of dst t fow fd t tod dostts sow t of cogc t t ow Mc bs d fs so css. Ts bo c b d b t o of t ss costcto t c fcs t gt d sd of qtos. Ts o s t s wt codtog s sd o ot. I t st tcq ss s cctd t c fcs ts of t cost bs g t c ods t qto of stt. So t ss costcto o s t s od of gtd s dst d g tt. At ow Mc b wtot tg dst s costt. T t tos of dst d g t fow od OM c t ss costcto o s of t s od s t tos of ss t fow fd d t c tod woks w. If dst d tt ot o d to cossbt bt so d to stog tg d ts to s O t ss costcto o s od of gtd O w t ss to t fow fd s OM. To so ts ob o c obt ss t c fcs ot fo t qto of stt bt fo t soto dct.. ss st b o of t ddt bs t ss costcto o tks to toto s OM. It s ott to cos c oto t gt d sd of t gog qtos t t s t. T odfd tod ss T s ddt bs d t f oto sd s s foows: 4 4 k k k k o o A o MP S S S > < > < F F F 3.7 w U M W W P P F A AM c c c c M 3.8 w

11 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S c P β β Uk t og so dscbd bo ts odfd foto of ct Ht- Y sc fo bt qto of stt g t fo s fod to b stb t Mc bs cdg t ow os. 4 QUILIBRIUM DISCHARG GASDYNAMICS & LCTRODYNAMICS W ss sbsoc fow cdc dscg c s stto d stc o wt sw zt dcto. Hg fqc ctogtc fd dos ot fc gs tsot ots dt ocsss ggb d t fow s d LT. To st t fow w s f N-Stoks qtos wtt cdc coodt sst wt ccot fo t oct coots - d d so tgt o d to t fow sg togt wt t g qto wtt fo t tot gs t. Ts qtos cd soc ts cosodg to ctogtc fd fc: Lotz foc coots so cd gtc ss d Jo t odcto. Bod codtos fo N-Stoks qtos foowg: css fow ts scfd t t sot t t c t scto; oct coots q zo t gd sfcs; w kow "soft" codtos d t t c t scto; st codtos d t t s. Sos tt osctg t ct st dcto cc cos odcs oocotc ctc fd wt co td H z. Foowg Boos w s t ssto fo tgt coot of t ctc fd td z: / z << / tt ds to qs-d oto of Mw qtos: d ωµ σ H d d ωµ d d 4. z d H z d d d coodts; ω πf s cc fqc of oocotc ctc fd σ s s ctc codctt µ s c gtc c H z s co td of gtc fd coot. I ts oto t coot of Lotz foc qs zo. Obtd qs-d oto s sst sfcto fo t ob t ds to bod ob fo t od dfft qto wtt bo to dt t co td of otc ctc fd z; z coodt s t o ts qto dds o z owg to bod codtos. To dt w s so st codto t t s z d t codto t t dscg c w 34 s foows:

12 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S ωµ H z d R : c zc d 4. H R c s t c ds H z s t td of gtc fd coot t t c w odcd b t dcto RF ct otsd t s fow. T coso of t f two-dso Mw qtos sotos wt t qs-d oto sts std 5 sowd good ccc of ts oto wd g of otg fqcs fo t s toc got d cosdto. 5 CALCULATION OF PLASMAS TRANSPORT PROPRTIS To so t N-Stoks d Mw qtos tsot coffcts css: scost t codctt d ctc codctt. I o tod tsot coffcts w cctd dc fo t qb s fows s fctos of ss d tt. T ffcts of o-d gs d s w ot ccotd fo. T tsot ots w cctd b t cs fo of C-skog tod 8 t tt g 3 T 5 K fo dfft gss: tog og go cbo dod. Ccto tcq d ot sts fo tsot ots d LT w std os 6. T fst o-zo oto s t cct to cct tsot coffcts fo t gss bt fo ozd gss t c d to 5% o 67. O cctos fo g tts w d wt ζ fo scost d ζ 4 fo ot tsot coffcts to od 5% ccc ζ s t od of oto b So oos.. b of ts So oo sos of Botz s qto soto tt od tsosto t C-skog tod. otd fo 8 fo tsot ots o cot fo cctos t t cssc fo 78 of C-skog tod bcs t tt fo o coctd d s g od dtts: Nζ Nζ std of Nζ- Nζ-. scost µ ffct t codctt λ ff d ctc codctt σ cctd t -d µ d 4-t oto λ ff d σ t P. t fo t f gss std Fg T cs fo λ ff sow dffc btw go ow c wtot ks t T<K d t oc gss wt o tog d og o two d CO ks d to dssocto t T<K. A ctc codctt s g t tt of t ot gss t ow tts: 3 T 6 K. Bt t g tts 6 T 5 K cbo dod ctc codctt s g t tt of t ot gss tog ts tt g t dffc btw ctc codctt of tog og d go s ot g ss t t dffc btw t 4-t d -d otos fo c of t gss. Ts totc sts b cod wt ot cottos obtd t t KI d wt b t dt t b g fo t sto tts 9.

13 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S.5 O O g Ago µ C O A Ntog T K 5 Fg 3.: scost P*s/ fo f gss: tog og go d cbo dod cctd t scod o-zo oto λ 5 ff O O g C O A Ntog 4 3 Ago 5 T K 5 Fg 4.: ffct t codctt [W//K] fo f gss: tog og go d cbo dod cctd t td o-zo oto 3

14 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S σ 3 O O g A g o C O A N t o g T K 5 Fg 5.: ctc codctt [/O/] fo f gss: tog og go d cbo dod cctd t td o-zo oto 6 ICP FLOW SIMULATION RSULTS Cctos of qb tog og d go s fows fo IPG4 dscg c got 3 wt t c ds R c.4 d gt Z c.46 w fod. T ft-o tod bsd o t ct TD Ht-Y sc d SIMPL got of Ptk d Sdg og wt t d-to ocd to cs stbt w sd to so t N-Stoks qtos. A ofo gd scg of 3 b 43 cs t d d dctos ws sd t cctos. T of RF dcto ct s dtd t soto ocss w t ow t s N s scfd. Cctos fo t f gss w cd ot fo t sg sto otg g: gs fow t G.8 g/s wt 45 dgs t sw ss P. t N kw fqc f.76 MHz. T w tt of bot t qtz tb d sfc of t gs jcto tfc ws T w 3 K. Fg. 6 sows t cotd sts d tt fds wt t IPG-4 dscg c fo. I t Fg. 7 t ofs of tt TZ c t t c t scto std fo t f ss. Ago tt of s c g t tt of ot gss. T ow ffct t codctt of go s ds to sst dffc tt fd wt t c tt d t fo go s s sftd sst fo t s to t w d tt gdts wt f b c ow t tt fo t oc gss. 4

15 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S Z Fg 6.: Sts d sots fo IPG-4 s t P. t G.8 g/s N kw f.76 MHz T K Ago 8 O 6 4 CO A N 3 4 R Fg 7.: Tt T [K] t IPG-4 c t scto fo f gss: tog og go d cbo dod T ssoc otfow fo t IPG-4 sto tog L ozz to t tst 5

16 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S cb ws cosdd so. T t ts of t ob s foows: gs s t t of t jctd gs d gs o t w s kj/kg t g of t fow sg s 45 t oto fqc s 76 MHz ow s kw t costo of t jctd gs s 8* -3 kg/s. Pss ws st 3 P o t sbsoc ott bod t tst cb. Ts fcto ws ctd t tst cb. Mc bs cgd fo * - t cctd fow to 5 o t ozz d. I t Fg. 8 t t cosods to sts t ow t t t dstbto. T ss ws bot 7 P o t ozz d. Ts t jt s odd ts cs d t otfow s ccod b t tc sst of socks d fcto ws. A fow tt t ozz cdg t fst two csks s std t Fg. 9 b t dstbto of ss. T oct ws bot 3 /s t. A cctos w fod b t q wtot ddg to dfft ts H: dstc Fg 8.: Ssoc otfow fo IPG-4 sto. T t cosods to sts t ow o t dstbto dstc P Fg 9.: Otfow to tst cb. Pss dstbto P 6

17 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S 7 COD-TO-COD ALIDATION A coso of sts obtd b t bsot dfft cods ws do fo s otg sss ;.;.4 t t cs of go. W sd t cods tod bo cod d. As w w st t sts 5 obtd t t o K Isttt sg t cod dscbd 7. T sts obtd b cods sob good gt. Fow got bod codtos s t s s bo. T s of sc coso std Fg. -. Otg ts s foows: t costo s.8 g/s t otg ss s.t t otg ow: 5 kw. Tt ofs t ostos 5 s t go 7 s d-co d 46 s ott std Fg.. Tt fds d fow stcts fo bot MIPT d IPM sts std Fg. -. T s gt of t cotto sts s obsd fo ot ss ts. Ago P. t 9 K t KI Dstc fo s Fg : Coso of tt ofs t 5 c 3 7 c d 46 c 7

18 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S MIPT T: A dstc Ago 5kW P.t Fg.: Tt fd d fow stct sts: cod MIPT IPM T: A dstc Ago 5kW P.t Fg.: Tt fd d fow stct sts: cod IPM 8 CONCLUSION A sco-cc od c tod d cotto sts fo qb dct cod s fows sto w obtd. A dcd tcoog dod fo cctos of t s tsot coffcts bsd o t goos odfcto of t C-skog fos d ot dtbs fo todc d tsot ots std. A w ffct codtog tcq og wt ct TD sc ws dod to so t N-Stoks qtos bot sbsoc d ssoc gs fo. Cctos w fod b t fo wtot ddg t do stgtd to dfft ts. Cod-to-cod dto ws fod fo dfft t ts. A good gt tks c fo t sts obtd b t dfft cotto tods. 8

19 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S 9 ACKNOLDGMNT Ts sc ws sotd b t INTAS d RFBR gts INTAS-RFBR INTAS-SA RFRNCS [] A.N. God A.F. Kosko d M.I. Yks M.I. A Idcto Psto Acto to B s Ht Potcto Ts God Tsts SAMP J [] A.F. Kosko T Aotodc Sto Sb- d Ssoc Hg- t Jts: t d To Poc. of t Scod o Sos o Aotodcs fo Sc cs STC Noodwjk T Ntds Nob 994 SA SP [3] M. Awt-Ktz F. H G.Hdc H. Ktz T. L. Scb d T. Wg T God Tst Fcts fo TPS t T Isttt F Rft-sst 3d o S. o Aotodcs fo Sc cs STC Noodwjk T Ntds Nob SA SP [4] B. Bott M. Cboo. D Hg d S. Ps Pdctd d Msd Cbt of t KI. MW Psto Rgdg R-t Sto 3d o S. o Aotodcs fo Sc cs STC Noodwjk T Ntds Nob SA SP [5] A. Kosko M. Yks I. Ps d S. s sk Ht Tsf Sto d Sfc Ctct Pdcto t t Mt Atos t Codtos AIAA P [6] A.F. Kosko I.S. Ps S.A. s sk d M.I. Yks Std of Qtz Sfc Ctct Dssoctd Cbo Dod Sbsoc Fows J. of Sccft d Rockts [7] D. d Ab d G. Dgz Nc Mod of Hg-Pss A Idct Pss d T d Cc Noqb AIAA P -46. [8] A. F. Kosko d G. A. Tsk qtos of Hdodcs fo Pt Iozd Mt-Coot Mts of Gss og Hg Aotos of Tsot coffcts t. fo Rss. I: Fd Mccs-Sot Rsc Sct Tcc Ic [9] S.A.s'sk A.F.Kosko S..Utzko d G.S.R.S Psco-cc Dt Bs d Cotto Rsts fo Idct Ps Fows. I: Pogss Ps Pocssg of Mts ds. P.Fcs d J.Aoo Bg Hos Nw Yok

20 Sg. Utzko Ad.Koko Ds.Rdko Sg A. s'sk Ato F. Kosko d G.S.R. S [] C.ozt Ict Uwd Scs fo Low Mc Nb Cossb Fows Tcc Rot 384 INRIA 997. [] H.C.Y R.F.Wg d A.Ht Ict Tot to Dsg Scs fo Std- stt Cctos. J.Co.Ps [] M.I.Boos M.I. Gg R. Bs R.M. ffct of sw d coft o t fow d tt fds dct cod.f. s T Cd J. of Cc gg [3] s'sk S.A. Kosko A.F. Yks M.I. Mttc ods fo s d gs fows dcto stos Moc Pscs d Hsoc Fows d. b M.Ct NATO ASI Ss Kw [4] Mko B.P. Nc odg of g fqc dcto dscg go. I: So obs dodcs oscs d d ccs. Moscow MIPT Rss. [5] D. d Ab S. A. s'sk A. F. Kosko G. Dgz B. Bott Cod-tocod dto of dct s cottos. I: Pogss s ocssg of ts ds. P.Fcs d J.Aoo 45-5 Bg Hos N.Y [6] S.A.s sk I.A.Sokoo G.A.Tsk Dtto d ccto of tsot coffcts fo cc qb t ozd d f ozd gs fows J. of Ad Mccs d Tcc Pscs Rss. [7] M.Ct R.S.Doto Tsot coffcts of g tt tog Pscs of Fds [8] J.H. Fzg d H.G.K Mttc to of tsot ocsss gss Not-Hod Pb. Astd-Lodo 97. [9] B. Bott D. d Ab M.Cboo G. Dgz G.S Todc d tsot ots fo dct s odg J. Tos. Ht Tsf