Ondes et stabilité dans les solides

Texte intégral

(1)Ondes et stabilité dans les solides Michel Destrade. To cite this version: Michel Destrade. Ondes et stabilité dans les solides. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2007. �tel-00192249�. HAL Id: tel-00192249 https://tel.archives-ouvertes.fr/tel-00192249 Submitted on 27 Nov 2007. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2)

(3)

(4) !"# $%'& *( ),+.-/102'/1354"687:9/<; =>7@?BA<687C4AD)E65/F9G/H(IA 9J10E),3"7K4")LADMN/1MO(IJ1+17@M),PRQG/<; STM)LU</1638)L4JWVX)E/1665//Y4(Z7:6)L/W[\Q6)L/<;$V!7:6),3']^ _a`bcedgfhjilkLmneo dqpd,r nsrXdtcuwvyxWdqfzdt{#h|fi}h~Ihzhf>!!h~ R J1+Y),7@0E)L4J _a`|neuXdt!h 9GJ1+Y/1 ?65/C<@].

(5)

(6)

(7)

(8) .

(9)

(10)

(11) . ! " # $&%(')+*-,/.0%)1.0*2%,0*43./5.637,0./%)8.0 9 :+;=< >@?1A1BDCEA1BFHGJIKLBDMLN!OQPSRUTV1TXWTXYUT<:+TZ<7[]\^;_;;_;;;_;;_;;`;_;;;a<7: :+;b: >@?1A1BDCEA1B_cdfe!?UBgKLB4IQPh<7iUTX:j[+TXklR]\E;;_;;`;_;;_;;;_;;_;;`;_;;;a<JR :+;mR >@?1A1BDCEA1B_c+noO1e!K=dfB&P=<JR]\p;;_;;_;;;_;;`;_;;_;;;_;;_;;`;_;;;a<7q :+;SV >@?1A1BDCEr1MLsDtge]uvGjnge!wUCxdfMzy8w1BgCPh<W+TX:!qTR!iUTXk{q\ ;_;;;_;;_;;`;_;;;a<7W :+;bq >@?1A1BDCEAGj?1CEKLBDCEC|e!KzMLA1BDCE}~NjfGjA1MzBg?5dEA1B`r1xe!r1|MzsDd|sgCPb:]YUTR5:\;_;;;a<7W $&%(')+*-,/.0%)U].0*g8*% ,0*43./5.637%) %f,/.0%(8. # RU;=< >@?1A1BDCHAZmMz?8d|Bg0GjngBAGj?1CKLBDCEC|e!KzMLA1BDCMz?1ngej-r1xBgCxC|MLUKLBgCPm:jiUT:+<jTZ:]RUT R!R\;_;;;_;;_;;`;_;;;_;;_;;;_;;`;_;;_;;;_;;_;;`;_;;;:]R RU;b: >@?1A1BDC_AZmMz?8d|Bg0GjngB&AGj?1C_KLBDC_Cxe!KLMzA1BgCGJ!BDnKLMLGjMLCxe!?ML?5d|Bg|?UBPSUT<j<!T <qTX:!:+TXk{:\;;_;;`;_;;;_;;_;;;_;;`;_;;_;;;_;;_;;`;_;;;:jq RU;mR >@?1A1BDCEA1Bp!e!Kzw1-B~Pmq+TX[UTZ<7Y]\;_;;;_;;`;_;;_;;;_;;_;;`;_;;;:jq 371./,0.637+%,*D3.05.637%(%o,0./%)8. #X9 V1;=< v?1CdoGjUMLKLM=dfsHAmwU?1B_&Bg21fGj?UBpC|r1O1sD|MzywUB_BD? Mz?U¡XG]d|MLe!?PSRU<g\H;`;_;;;^Rji V1;b: v?1CdoGjUMLKLM=dfs¢CxdoGdfMLy8w1BEA1BECxw1x0GjnDBEBDd£ASML?5dfBDx0GjnDB_Ph<!<!T<7q+T:jiUT:+<jTU:j:+T :jR+TRU<!TXk{:\;;_;;`;_;;;_;;_;;;_;;`;_;;_;;;_;;_;;`;_;;;^R+< V1;mR v?1CdoGjUMLKLM=dfsHAUI?Gj&MLy8w1BÀSML?5dfBDx0GjnDB-PSR!R]\¤;_;;_;;;_;;_;;`;_;;;^R!: ¥ $&%(')+*-'£¦h§©¨ª,0.37«')¬ª%(.0 " q+;=< >@?1A1BDCHKzML?1sgGjMLxBgC{BD?sgKLGjCxd|MLnDMzdfsp?Ue!?+uvKzML?1sgGjMLxBPh<!T:+T)<JV1T<7+TZ:V1Tk<!T kVj\2;_;;;_;;_;;`;_;;;_;;_;;;_;;`;_;;_;;;_;;_;;`;_;;;^Rj q+;b: >@?1A1BDCE?1e!?+u®KLML?UsJGjMz|BgCAGj?1CEKLBDC{C|e!KzMLA1BDC{A1MLCxr BD|CxMzC`Pm:jUTkVj\;`;_;;;^RjY ¯ @8*g¨°j3.6±+* [U;=< ²°|ejKLe!?1NjBg&Bg?5d{A1BDCd|fGJ]Gjw+³BD? nDe!w1|C´;`;_;;_;;;_;;_;;`;_;;;µV!R [U;=<!;=< >@?1A1BgCE?1ej?+uvKzML?1sgGjMLxBgC;_;;;_;;`;_;;_;;;_;;_;;`;_;;;µV!R [U;=<!;b: >@?1A1BgCEKzML?1sgGjMLxBgC¶;_;;_;;;_;;`;_;;_;;;_;;_;;`;_;;;µVjV q.

(12) GjUKLBpA1BDC-G]d|M gxBgC [+; : He!wUjBgKzKLBè!|MzBg?5doGdfMLej? K G1Mze!-sDnJGj?UMLy8w1Bp?1e!?uvKLMz?1sJG]ML|B ;_;;;_;; V8q [U; :;z< ke!?5d|B4³dfB_BDdEBg? xBgw+³ ;;;;;_;;_;;;_;;_;`;;_;;;_;; V8q [U; :; : s4dfO1eA1e!Kze!N!MzB@N!sg?UsgfG]KLBpBDde! xBgnDd|MzC~;;_;;_;`;;_;;;_;; V5 [U; :;bR ª³+Bg&r1KLB < sDnJGj?1Mzy8w1B A1B KLGrBJG]w¤O8w1G]ML?1B&BDdAUBK G rBJGjw GjdfM 1ngMLBDKLKzB ;_;;;;;;_;;_;;;_;;_;`;;_;;;_;; V5Y [U; :;mV ª³+Bg&r1KLB_: v?1CxdfGj1MzKLMzd|sA1BDCG]?1sD|MzC|&BgCGje!dfMzywUBgC ;;_;;^q+< [U; :; q ke!?UngKLwUC|MLej?;;_;;_;;;;;;_;;_;;;_;;_;`;;_;;;_;;^q!: . . . . . . .

(13). [. .

(14) £

(15) Gj?1C KLG©r1xsD0GjnDBA1B Cxe!?KzMz|B]T ML?1N <7YjY![B4³+r1KLMzy8w1Bre!w1xywUe!MMzKKzw1MEC|BD1KLB y8w1B- BgGjw1nDe!w1r AUBr1xe!1K D-BDC`C|e!?5d_r1KLw1C`0GjnDMLKLBDC}xsgC|ejw1A1|BGj?GjK=I8dfMLy8w1BD-BD?5d_BD? sDK GjCdfMzngMzd|s

(16)

(17) y8wmBD? sgKLGjCxd|MLngM=dfs{MzC|ejd||e!rBj;jBHrGjdoGjN!BC|ej? GJ+MzC¢ngGjnDe!&-B Kzw1M xB~&BC|w1MzCMz?5dfsgxBgCxC|s } K/msDK GjCdfMLnDMzd|sGj?1MzC|ejd||e!rBCfG]?1C2GJje!MLps4dfw1A1Mzs~KSsgK G]CxdfMzngM=dfs KzML?1sgGjMLxB MLCxejdfxe!r B]; |e!w+!Bg-w1?1BC|e!KzwUdfMze!? Gj?GjK=I8dfMLy8w1BBD?sgKLGjCxd|MLngM=dfsGj?UMLC|e]df|ejr B ?ZmBDCxd{rG]C¢noO1ejC|BpGjMzC|sDBjTU-GjMzC£nDe!&-BEKSB4³+r1KzMLy8w1B ML?1NUT+BD?dfxe!wU!BDK/msDywUMz]GjKLBD?5d¢BD? sDK GjCdfMzngMzd|s_MzC|ejd||e!rB2BDCxd`w1?rU|engBgCxC|w1C`y8w1M ?UBC|BA1sD|e!wUKLBrG]CpGjwUd|e!GdfMLy8w1BD-BD?5dJT r1Gj°w1?1BEC|rsgnDM GjKzMLC|G]dfMze!?A1BDC£nDe!?1CdoGj?5dfBDC¢sDK GjCdfMzywUBgC ªBD?-BZB4dJT8KSsgKLGjCxd|MLngM=dfs¢MLC|e]df|ejr B BDCxd !" rGj{|Gjr1re!xd}K/msDK GjCdfMLnDMzd|spGj?1MzC|ejd||e!rBjT+BDd|BDywUMLBgdr1KLw1C{AZmBZe!dfCD;

(18) B£0G#gej?C|Mz-MzK GjMz|BjT xB¢&B¢Cxw1MLCML?5dfsD|BDC|C|s}HK/msDK GjCdfMLnDMzd|s

(19) $&%(' )! ) C|Gj?1CªG7je!ML s4dfw1AUMLs KSsgKLGjCxd|MLnDMzdfs&KLMz?1sJG]ML|B];©vK mG C|BD1KLs y8w1BKzBgCsDyw1G]dfMze!?1CA1w -ejwU!BD-BD?8d s4doGjMzBg?5d nDBgdfBgCnge!&r1KLMzy8w1sgBDC* A1BgC CICxd D-BDC nge!wUr1KLsDCASsgy8wG]d|MLe!?UC Gjw+³ A1sD|M=!sgBDC r1Gjxd|MLBgKzKLBDC?1e!?uvKLMz?1sJG]ML|BDC°G]MLC DmGjMZGjr1r1xsgngMzspK G2nDe!?1Cxsgy8w1Bg?UngBr1|Mz?1ngMzrGjKLBHA1BpngB4d|d|B nDe!&r1KLB ³UM=dfs °Bg?B+ BDdJTMLKXB ³UMzCxd|Bdf gCrBgwA1BCxe!KLwUd|MLe!?UC¢B ³1G]nDdfBDClBg?sgK G]CxdfMzngM=dfsE?1e!?+u KzML?1sgGjMLxBjTBDd{ej?rBgw+d{Bg? 0GjMz|B@|Gjr1MLAUBg&Bg?5d{KLBHdfe!w1D; ²ªGjnge!?5df|GjCxd|BjTKzB@rGJICfGjN!BpAUB K/msDK GjCdfMzngMzd|sKzML?1sgGjMLxBMLCxejdfxe!rBpCgSsDdfBD?1A }rBgdfBÀ1Bpw1Bj; °?1nDe!|Bp}_ngB xejw1gT+Gnge!?1?1GjMLCxCfGj?1nDBA1BKSsgK G]CxdfMzngM=dfs{KLMz?1sJG]ML|BEMzC|ejd||e!rBHBDCxd{KzMLu M=dfsDBj; °?&|B4jG]?1noO1BjTMLK+-B{CxBgUKLB-,Dd||BE1MzBg?&Gjw0GjMzdªA1w&rGjC|CxsEBDd A1BEKmGjn4dfwGjKzMzd|sA1BDC AUe!G]ML?1BDC°Gje!|A1sDC°AGj?1C°nDBDdxdfB{A1MzC|C|BDxdfG]dfMze!?T5}pCfGJje!ML K GrU|e!rG]N5G]dfMze!?A1BDC e!?1A1BDC BD?-sDK GjCdfMzngMzd|sKzML?1sgGjMLxBlGj?1MzC|ejd||e!rBjT5KLG@r1|ejrGjN5G]d|MLe!?2A1BgC£e!?1A1BDC KLML?UsJGjxMLC|sDBgC°G]w~je!MLCxM=u ?1GjN!BASw1?1B~N!|Gj?1A1BA1s4e!|-G]d|MLe!?T K GCdoGjUMLKLM=dfs_ML?1nD|sg&Bg?5dfGjKLB]TBDd`KLG r1|e!r1GjN5G]d|MLe!? AUBgCpe!?1AUBgC@sDK GjCdfMLy8w1BDC@AmGj&r1KLM=dfw1A1B ?1MzBj;/.BgCpnoO1Gjr1Mzd||BDC@y8w1MªCxw1MzjBg?5d`r1|sDC|BD?8d|Bg?5d &BgCEnDe!?5df|Mz1wUd|MLe!?1Cl}&nDBgCEA1e!-GjML?UBgCg; ²°w1MzC@+MzBg?5dpKzB|sDnJGjr1M=dfw1KLG]dfM=°A1B&e!?QGjn4dfMzM=dfs2CxngMzBg?5dfM y8w1B~GjwQnge!wU|CpA1BDCpC|Bgr+d AUBg|?UM gxBgC Gj?U?1sgBDCg;10nDBDd|d|BGjnDd|MzMzd|sjT DmGjCxC|engMLBlG7jBgnEK G@rUKLw1C NjfGj?1AUBlN!fGdfMzd|w1A1Bl&BgC G]-MzC2]nDe!KLKLGj ejfG]d|Bgw1xC¢B4dH-G20Gj&MLKzKLBj; . . . . . . . . . .

(20).

(21). . . W.

(22) . <!;²°|s40GjngB.

(23) . . . . & . °?¤sDK GjCdfMzngMzd|s-KzML?1sgGjMLxBjT)e!?¤?UBngej?1C|BDx!B y8w1BKLBgC_y8wGj?5dfM=dfsgC2ML? ?UMzdfsDC|MzGjKzBgCpB4dK G Ur |e!rG]N5G]dfMze!?A1BDC_e!?UA1BgC`sgKLGjCxd|MLy8w1BDCBDCxdA1e!?Un&Nje!wU!BD|?1sDB-r1GjÀ1BgCsgy8wG]d|MLe!?UCpA1Mz u sD|BD?8d|MLBDKLKLBDC ' )!) ;ce!wU!BD?5d-ej?¤sgnD|Mzd2ngBDKLKLBDCu®ngMCxe!w1CKLG e!x-B&ASw1? CxICxd g&B AUM sg|BD?5dfMLBDK KzML?1sgGjMLxBEA1w C|BDnge!?1Ae!xA1|B];10Mz?1C|Me!?GUTAGj?1CKLBCICxd D-BpejxdfOUe!?1e!x-s xBgn4doGj?1Njw1K GjMz|B@AUBnDe+ej|A1e!?U?1sgBDC (x , x , x ) T :;biU;=< c u = ρu , C|ej?8d@KLBgCnge!&r ejCfGj?5dfBDC@A1w d|Bg?1CxBgw1pA1BDCp|MzN!MLA1M=dfsDCgT BDCxdpKzB e KLBgC AUsgr1KLGjngBDc-BD?8d2-sDnJGj?UMLy8w1BMz? ?1M=dfsDC|ML-GjK/TK GMz|N!w1KzB~A1sg?1e]dfB KLGuA1=sD|M=u(x, !sgBrt)Gjxd|MLBDKLKLB]T B4d ρ BgCxdEKLGG]C|C|B@je!KLwU-MzywUBA1wC|ejKLMLAUBj; vnDMKLBd|Bg?1CxBgw1EA1BDC{|MLNjMLA1M=dfsgC¢r ejC|C|sDA1B`KLBDC CI-s4df|MzBgCE&ML?1BDw1|BDC{BDdG xBgw1xBgCEC|w1M=]Gj?5dfBgCDT :;biU;b: c =c , c =c . ²°|BD?1e!?1CªGjMz?5dfBg?1Gj?5dªw1?UBe!?1AUBr1KLGj?1B£r1|e!Nj|BgCxC|M=!BMz?1O1e!&e!N D?1BjT]C|B¢A1sgr1KLG#JG]?8d GJjBgnKLG&Mzd|BgC|CxB v BDdKLB_?1e!1xB_AZme!?UA1B k A1Gj?1CKLG-A1Mz|BDnDdfMze!? x T BDdr e!wUHy8w1MKLBgC rUK Gj?1C{AZbGj&r1KzMzdfwUA1BgC{sDN5GjKLBDC{C|e!?5d?1e!xG]w+³} x TC|ejw1CEK G2e!x-B B /:+;bi+;bR u = U (kx ) + c.c., e ?1B A1sDr BD?1A`ywUB£AUB°K G]Gj|MLGj1KzB kx BDd vnj;Snj ; -BgCxd)K/bG]1|s4+MLG]dfMze!?@A1B°K/mB ³+r1|BDC|C|Mze!? U vnge!&r1KzB4³+Bngej? xw1N!w1 s o; .BgC`sDyw1G]dfMze!?1C :;biU;=< HCxB~|sgAUw1MLCxBg?5d_GjKLe!xCp} w1?CxICxd g&B AUB_RsDyw1G]dfMze!?1CEA1M sgxBg?5dfMzBgKzKLBgC

(24) $ ) ) T1AUwCxBgnDe!?1Aej|A1xB M /:+;bi+;mV T U − (R + R

(25) )U + (Q − ρv I)U = 0, e KzBgCE-G]dfxMLngBDC T T Cxe!?5dHAUs ?1MzBgCrGj{KzBgw1{nDe!-re!C|Gj?5dfBgC /cdfxe!OT<7Y![!: 4T T R Q :;biU;bq T =c , R =c , Q =c . Y.

(26). . . 1. 2. 3. ijkl l,kj. ijkl. i,tt.

(27). . ijkl. klij. ijkl. jikl. . 1. . 1. k(x1 −vt). 2. 2. . . . 00. 2. 0.

(28). ik. i2k2. ik. i1k2. ik. i1k1.

(29) :+;X>@?1A1BDCHKzML?1sgGjMLxBgCBD? sDK GjCdfMzngMzd|s@KLMz?1sJG]ML|B ?&noO1BD|noOGj?5d{wU?-&e+AUB{rGjxd|MLBDKC|e!w1C e!x-B{B ³Ure!?1BD?5dfMLBDKLKzB U (kx ) = U B T e U BDCxd`w1?jBgnDd|Bgw1`nDe!?1CxdfGj?5dBDd q w1?1B~y8wGj?5dfM=dfsnDe!-rUKLB4³+B]Te!?Gje!wUdfM=dp} KLG

(30) $

(31) $

(32)

(33) $ :+;miU;m[ AUBDd [q T + q(R + R

(34) ) + Q − ρv I] = 0. kB4d|d|B2sgy8wGdfMLej?T AUMzdfB vA1BkO1xMLCdfe BgK oTBgCd@w1?r e!K=I? &BBD? }-nDe+B &ngMLBD?5dfC |sgBDKLCD; ?©N!sg?UsgfG]KT(MLK°CgmGjN!M=dAmwU?1B T(KLej|C|y8wmGjw1nDw1?¤A1BDCGq³+BDC x T x T x ?mBDCxdlGjKLMzN!?1sGJ!Bgnw1? G³+B@A1BHCxI&sDdfxMLBA1w -G]dfsD|MLGjw* e!w 1MzBg?-C 1DTUC|MKLB-G]dfsD|M G]w ?1B@re!C|C gA1B`GjwUngw1?1BpCI-s4df|MzB ; c+BgC{|GjngMz?1BgC?1B@rBgwUjBg?5dA1e!?1n ,4dfxB@B4³+r1xML&sgBgCA1B 0G#ge!? Gj?GjK=Id|MLy8w1B]TUAmGjr1 gC{K G`dfO1sDe!|MzBA1B `GjKze!MLC BJGjAZT<7Y5WjY 4; >@? rBgwUdlGjKzN!|s dfe!wUdEejUdfBD?1ML{A1BDCHxsgCxw1KzdfG]dfCEB4³+r1KzMLnDMzdfBDC{AGj?1CEnDBgxdfGjML?UBgCEngMz|ngej?1CxdfGj?1ngBDCHB4dE|sDC|e!w1AU|B Bg?5dfM g|BD-BD?5d¢nDBgdoGjMz?1C r1|e!UK g&BgC£Gjw³~nge!?5d|e!w1|C£CfG]?1CGJje!ML BgC|ejML?&A1BgC£fGjnDML?1BDC A1B K GC|B ³dfMLy8w1B]; .°SB4³+Bg&r1KzBEGj|noO1s4dvIr BEA1B{nDBldvI+rBEA1B{r1xe!1K D-B¢BgCd¢KLG|BDnoO1BgxnoO1BA1B '

(35) $ '

(36) $ ' $ - w1?1BEsgy8wG]d|MLe!?&A1e!?5d KLG+M=dfBDC|C|BBgCd K G ' ML?1nDe!?1?8w1B 4; kB4d|dfBywUBgCxd|MLe!?Ge+nDngw1rsAUBl?1e!U|Bgw³2noOUBg|noOUBgw1xC£rBg?UAGj?5d r1KLw1CxMLBDw1|CA1sDngBg?U?1MLBDCgTpngej-&BKmG¤fGjnDe!?5dfs ML?1N AG]?1C wU? GjdfMzngKLB|sgngGjr1M=dfw1KLG]dfM= :ji!i]V a4; .(G_|sgwUC|C|M=dfB@KLG_r1Kzw1ClG] e!w+dfMLBAGj?UCngBA1e!-GjML?1BEBDCxd{KLG_&MLC|BHGjw re!Mz?8d¢A1w e!|-GjKLMzC|&BHMz?5dfsgNjfGjKAUB Gj|?1B4d|dBDd .ejd|O1B <7Y!!q 4T+ywUM(CDbG]r1r1w1MzBpC|w1KLBDCldffGJ]Gjw+³ r1MLe!?U?1MLBD|C£A1B`cd||e!O <7Y![5: ;°kBpA1BD|?1MzBgG2ML?5dfxe+AUw1Mzd¢KLBDCdf|GjnDd|MLe!?1C£CgSB4³+BD #JG]?8dCxw1 KLBgCr1K Gj?UC x = nge!?UCxdJ; 0?1ej|-GjKLBHe!|MzBg?5dfsDB!BD|CEKLBDC x nD|e!MzC|C|Gj?5dfC£C|e!w1C{KLG_e!x-B M M B + c.c., :+;miU;bW σ = −c u = kt ( x ) e M /:+;miU;b t = T U − R

(37) U ; r1w1MLCG2df|Gj?1Cxej|&s /:+;bi+;mV Bg? w1? CICxd D-BpAUM sg|BD?5dfMLBDKZA1wr1|BD-MzBgej|A1xB@r ejw1KzB !Bgn4dfBDw1}~[~nge!&re!CfGj?5d|BgC ξ = [u, t]

(38) ;10HML?1CxMT /:+;miU;mVBgCxdsDywUMz]GjKLBD?5d} M e /:+;miU;bY N N ξ = N ξ, N= , N + ρv I N

(39) BDd /:+;miU;z<Ji N = −T R

(40) , N = T , N = RT R

(41) − Q.

(42) B ?1e!21|BDw+³xsgCxw1KzdfG]dfC-A1sgnDe!w1KLBD?5d A1B nDBDd|d|Be!xw1K GdfMLej?; ? rGjxd|MLnDw1KLMzBg&e!? df|ejwU!B_ywUB_K/msDyw1G]dfMze!? AUB2K GMzd|BgCxC|B2AUBgCej?1A1BgCHA1BC|w10GjngB_r BDwUdCxB2&BDdxdf|BC|ejw1C K G2e!x-B A1BDd M (v) = 0, :+;miU;=<!< e M (v) BgCdHKzB & TUA1e!?5dKLBpAUsDdfBD|&ML?G]?8dgT|sDBgKTBDCxdw1?1Bè!?1n u dfMLej? &e!?1e]dfe!?1BQA1sDngxe!MLCxCfGj?5dfBA1B v C|BDw1KLBD-BD?5d 0GjML?1CxMpK G¤Mzd|BgC|CxBA1B©K/mej?1A1BQA1B <7i. . 0. 2. kqx2. 0. . 2. 2. . . . 1. 2. 3. .

(43). . . . . . . . . . . . 2. 2. i2. i2kl k,l. i. 2. (x2 −vt). 0. . . 1. 0. 3. 1. −1. 2. −1. 3. 2. 2. 1. −1. . . .

(44) : ;>p?UA1BgCEKLMz?1sJG]ML|BDClBg?sgKLGjCxd|MLnDMzdfsKLML?UsJGjMz|B Cxw1x0G]ngBjT£y8wGj?1A BDKLKLB-B4³+MLCdfB]T¢BDCxd~KSw1?1Mzy8w1B fG]ngML?UB A1BngB4d|dfB sDy8wG]dfMze!? ; FEBgCdfB KLB ngGjKLnDw1KA1B |M (v)| TUy8w1MBgCd{KLejML?&A ,4dfxBdfxMzM GjK/T5G]MLC BgCd{?1sJG]?1-ejML?1C£r ejC|C|Mz1KLBGj?Gu K=I8dfMLy8w1BD-BD?5d{AGj?1CngBgdoGjMz?1BgC{CxMzd|wG]dfMze!?1C£A1BpCxI&sDd||MLB];£c+ML?Ue!? e!? wUd|MLKzMLC|BA1BDCldfBgnoOu ?UMLy8w1BgC?8w1&sg|Mzy8w1BgC_GJjG]?1ngsDBgCCgmGjr1r1wUI!Gj?5dCxw1_KzBe!|-GjKzMLC|&B2Mz?5dfsgNjfGjK lGj|?UBDd|d .ejdfOUBjT<7Yj5q £ejw C|w1lwU?1Bpsgy8wG]d|MLe!? AUB`FMznJG]dxdfM?1e!?+u®KLML?UsJGjMz|B MzxIw ]eT<7Yj5q w MLBDKjB]T(:ji!i5:4;_>@?©G]r1r BDKLKzB2KSsgy8wGdfMLej? :+;miU;=<!< 4TZK

(45) $ ' ASw1?1Be!?1AUBAUBCxw1x0G]ngBj; ?1BG]wUdfxBGjrUr1|enoO1BjTywUMHGGjw1CxC|M|B+#gw BJG]w1nge!wUr AmG]d|d|Bg?5dfMze!?T¢nge!?1CxMLCdfB } xBgnoO1BD|noO1BDKSsgy8wGdfMLej?AUB-KLGMzd|BgCxC|B&C|e!w1Ce!|&Bre!KzI?1e!&M G]KLBj;-kB4d|dfB&sgy8wGdfMLej? BDCxd&GjKze!|C2K G e!x-B fGdfMLej?GjKLMzC|sDB ~A1B K/msDy8wG]dfMze!?¤B ³1G]nDdfB /:+;bi+;z<!< 4;©kBDdxdfBy8w ,Dd|B AZmw1?r e!K=I? &BBDCxd?G]dfwU|BgKzKLBEBDd¢|BD-ej?8d|B@}K Mz?5!Bg?5d|Bgw1 AUBgCej?1A1BgC¢A1BCxw1x0G]ngBjT .e!xAFG7IKzBgMLNjO <J!5q Ty8w1MsgK D!BGjw nJG]||s2KLBgCHA1Bgw³ &BgU|BgCHA1BCxe!? sgy8wGdfMLej? B ³UGjnDd|B_BD? &MLKzMLBgw-MLCxejdfxe!r B]T}CfGJ!ejMLgT s s v v v :+;miU;=<: 2− 1− , =4 1− v v v e v BDd v Cxe!?5d KLBDC-Mzd|BgCxC|BgC AUBgC e!?UA1BgC A1B!e!Kzw1&B &B4d e!Ud|MLBD?8dCfG nDsgK g1xB nDw11MzywUB v v v v v :;biU;=<7R − 16 1 − = 0. −8 + 24 − 16 v v v v v .e!xC|y8w1B x T x T+B4d x C|ej?8dlGjKLMzN!?1sDCGJ!BDnpA1BgClG³+BgClA1BCxI-s4dfxMLBjTe!? ejUdfMzBg?5d{GjwUC|C|M wU?1B_nDw11MzywUB_BD? v /c!B 8KLe1T(<7YjV5 4; .e!|CxywUB2C|BDw1K x BDCxdGjKLMzN!?1s`GJ!BDn2w1? G³+B_AUB CI-s4df|MzBjT ej?¤e!Ud|MLBg?5d2w1?1B y8wGjdfMzywUB Bg? v /kw1|xMLBjT<7Y5Wj [ EPSR]\ 4; .)ej|C|y8w1B CxBgw1K BgCdGjKzMLN!?Us~G7jBgn&w1?¤G³UB&A1B&CxI&sDdfxMLB~e!?e!Ud|MLBg?5dw1?©r e!K=I? &BA1B-AUBgN!xs<7: x G]tgMLB4T <7Y!5W ZB4dpA1B ,g&B2CxM njSBgCd C|BDw1KLBD-BD?8d@ywUM BgCd`GjKLMzN!?1s_GJ!BgnwU?QG³+B AUB&CI-s4df|MzB ML?UN1T(:ji!ijV b ;

(46) Gj?1C`KLBDCx GjwUdfxBgC`nJG]C_e!?Qe!+dfMLBD?5d_wU?©re!KzI? -BAUB AUBgN!xs:!WBg? v GjtgMzBDT<7Y!jY4; MLBD?~Bg?5dfBD?1A1wT8A1B{?1ej1|BDw1C|BDC°fGjnDML?1BDC°rGj|GjC|M=dfBgC Cxe!?5dlMz?8d||eA1w1M=dfBgC£Gjw-nge!wU|CAUwr1xe+nDBgC|Cxw1ClA1BHfG]d|MLe!?1GjKLMzCfG]d|MLe!? r e]dfBg?5d|MLBgKzKLBD-BD?8d¢:][ G]xdfB40GjnDd|

(47) C kBDr BD?1AGj?5dgTMLK)BgCdpGJ]Gj?5doGjNjBgw+³ re!w1r1KLw1CxMLBDw1|CHfGjMzC|e!?1CA1BdffGJ]GjMzKLKLBD GJjBgnw1? re!K=I+? -B]; vK CDbGJ g|B`rG]xe!MzC¢y8w1B@K/msDy8wG]dfMze!?AUB@K G`+M=dfBDC|C|BBgCxdlw1? r ejKzI? &Bd| DClC|Mz~u • r1KLB]Ty8w1B~|MLBD??1BK G]MLC|CxBgHr1|sDCfGjN!BDGjw wAUBK G ngej-r1KzB4³+Mzd|s2A1BDC`sgy8wG]d|MLe!?1C A1B_kO1|MzCxdfe ZBDK; ejwUdfBDCKLBDC|GjngMz?1BgCHC|e!?5d@ejUdfBD?wUBgC@A1B_G]?1M D|Byw1GjC|MhuvML?UCxdoG]?8dfGj?1sDB2}&KmGjMLA1B • A1B~C|noO1sDGjC?8w1&sg|Mzy8w1BgCsgr1xe!wUjsgCgTªGJ!Bgn&KLBAUBgN!xs-A1B~r1xsgnDMLC|Mze!?QC|e!wUOGjMzd|sj; ²e!w1pCxsgKzBgnDd|MLe!?U?1Bg@nDBgKzKLB2y8w1MªBgCxdp]GjKzMLA1B]TZMzKCxw ~dÀmsDKLMz-Mz?1BgKLBDC@fGjnDML?1BDC nge!&r1KLB ³+BgC B4d KLBDC fG]ngML?UBgC v ?1sDN5G]d|Mz!BDCgT5r1wUMLCªAUBdfBDCxdfBD KLBDC fG]ngML?UBgCªxBgCdoGj?5dfvBDC G7jBgnKSsgy8wG]d|MLe!? AUBKLG+M=dfBDC|C|B`B ³1G]nDdfB]; <j< . . . . . . . . 2. 2. 2. 2 T. 2 T. 2 L. . T. 2. L. . 3. 2. 2. 2 T. 2 T 2 L. 2 T. 1. 2. 2 T 2 L. 2. 2 T. 3. 2. 3. 2. . 2. 1. . . 2. . . . . . . 2. 2.

(48) :+;X>@?1A1BDCHKzML?1sgGjMLxBgCBD? sDK GjCdfMzngMzd|s@KLMz?1sJG]ML|B. LM N!wU|B2:+;z< |ej?8d|C@ASe!?1A1B2C|w1pKLG-C|wUx0GjnDBAmwU?ng|MzCxdfGjKªA1B2ngw1M=+xB w1BDd

(49) B u C|noOGj&r1CDT:jijijV 4;{ke!-r1GjfGjMzC|e!?Bg?5d||B2KzBgC|sDC|w1K=doG]d|CHB ³UrsgxML&Bg?5doG]w+³ rGjML&rGjnDd K GjCxBg- 0}@N5Gjw1noOUB ªBDd KLBgCªr1|sDA1MLn4dfMLej?1C MLCxC|w1BDC°A1B{KSsgy8wGdfMLej?A1BlKLGHMzdfBDC|CxB{C|e!w1C ej|&B r e!K=I?1e!&M GjKzB 0}~AU|e!M=dfB ; e!wUdfBDC{KLBDClfGjnDML?1BDC{e!?5d{w1?1BpMz?5dfBgxr1|s4doG]d|MLe!?ZTUBDdEnDe!|xBgCxr e!?UA1Bg?5dH}A1BgCldvIrBgC • ASe!?1A1BDC@A1M sgxBg?5dfCD;

(50) B?1ej1|BDw+³B+ e!xd|C@ASMLA1BD?8d|M ngG]dfMze!?AUBngBDC@fGjnDML?1BDC e!?5dsDd|sBD?5df|BDr1|MzC G7IKze!gT_<7Y!U< GjtgMzBDT2<JY!5W !BDxI

(51) BDC|noOG]-r1CDT :ji!i!R 4; p nDBGjw r ejKzI? &BjTEe!?rBgwUdejUdfBD?1ML0G]ngMLKzBg&Bg?5d AUBgCB4³+r1xBgC|CxMLe!?UC G]r+u • r1|enoO1sDBgCAUB_KLGM=dfBgCxC|BBgKzKLB4u® ,D-B e!tDOGjB4 T(<7Y!Y+< !e!Mz|BÀGj?1CngBDxdfGjML?1BDC ngMz|ngej?1CxdfGj?1ngBDCgTA1BDCHB ³+r1|BDC|C|Mze!?1CB4³UGjn4dfBgC xPSY]\ ML?1NUTX:ji!ijV a4; 0KmGjMLAUB A1w r e!K=I? &Be!? r BDwUd d|fGjnDBgKLBDC C|w10GjngBDCA1BDCKLBg?5d|Bgw1xC ASw1? • ngxMLCxdfGjK G]?1MLCxejdfxe!r B2BDd`|BDnge!?UCxdfM=dfw1BD`KLBgC-ejd|MzC@AUBgCp|e!?5d|CpAmej?1A1BgC`B ³1G]nDdfB u -BD?5d HwUBDd

(52) BDC|noOG]-r1CDT:]i!ijV1TUje!ML MLN!w1xB`:+;=< 4; . . .

(53).

(54). . . . . .

(55)

(56)

(57) !#" !%$!'&(!)*!)+-,. ²e!w1`KzBgCè!?1A1BDC_AUB-FGJIKLBgMzN!OT)K G nDe!?1A1M=dfMLej?QGjw+³QnDe!?5dfe!w1xC_BDCxd_y8w1B-KzBgC

(58) $ A1MLCxrGjfG]MLC|CxBg?5d_C|w1K GC|w10GjngB&KLMz1|B~A1w©C|e!KzMLA1B&Gj?UMLC|e]df|ejr B]; 0Mz?1C|M MzK°C|Bg21KLB&r1KLwUC ?G]dfwU|BgK)A1Bpd|fGJ]GjMLKzKLBglG7jBgn_KLBgC{d|fGjn4dfMLej?1C :+;miU;mlywZbGJ!BDn2KzBgCA1sgr1KLGjngBD-BD?5dfCg;-UbGjM A1e!?1n@sDngxMzdlKzBgC¢sgy8wG]d|MLe!?1CA1w -ejwU!BD-BD?8dlC|e!w1C¢e!|&BASw1? CI+Cd D-BpASsgy8wGdfMLej?1C A1M sgxBg?5dfMzBgKLKzBgClAUw CxBgngej?1Ae!xA1|Bpre!w1 t T M ˆ + Rˆ

(59) )t + Qtˆ = 0, :+;=<!;=< Tˆt − (R <: . 00. 0.

(60) : ;>p?UA1BgCEKLMz?1sJG]ML|BDClBg?sgKLGjCxd|MLnDMzdfsKLML?UsJGjMz|B eKzBgCE-G]dfxMLngBDC Tˆ T Rˆ T Qˆ Cxe!?5dHAUs ?1MzBgCrGj

(61). :;z<!;b: ²°w1MzCgT}`KmGjMLA1B{AUBKLG@dfBgnoOU?1MLy8w1BHA1BgC£ML?5dfsDN!fG]KLBgC°rU|Bg&M D|BDC e!tDOGjBDT<7Y!Y5q4T5ngB4d|d|B ej|w1KLG]dfMze!?rBgx-B4d AmejUdfBD?1ML KSsgy8wGdfMLej?&AUBKLG@+M=dfBDC|C|BC|ejw1C°e!|&B{r ejKzI?1e!&M GjKzB Kze!|Cxy8w1B x BgCxdGjKLMzN!?1s&GJ!BDnw1? G³UB-A1B&CxI-s4dfxMLBjTr ejw1_wU? C|ejKLMLAUB&nDe!&r1|BDC|C|Mz1KLB PSRUT(Y]\°ejw©Mz?1nge!&r1xBgC|CxML1KzB P V1TW\;

(62) Gj?1C`KLBDCAUBgw+³QngGjCe!?Qe!UdfMzBg?5d`w1?1B&y8wGjdfMLy8w1B BD? ρv ; w /:ji!i!R{Gr1Kzw1CdfGj|A Gjr1rUKLMLy8w1s@d|BgKzKLBpy8w1BgKzKLB`ngB4d|d|Bd|BgnoO1?1Mzy8w1B_re!w1Ew1?UB ej?1A1B2AUB2e!|A He!?UBg?]eT <JY![!i{KLe!xC|y8w1B_K G~r1K Gjy8w1B_BgCdprGj|GjKLK gKLB`}&w1? r1KLGj?AUB CI-s4df|MzB K/msDyw1G]dfMze!? A1BKLG-Mzd|BgC|CxBCgmGJ gxB ,DdfxBw1?1BnDw11MzywUBBg? ρv TGjKze!|CHywUB K/msDy8wG]dfMze!? A1B_kO1xMLCxd|e BgKBgCdw1?1Byw1Gjxd|MLy8w1Bj; ²GjHKLG&Cxw1Mzd|B DbGjM)xsJGjKzMLC|spy8w1B_KLBDCsDy8wG]dfMze!?1CngKzBDCr e!wUejUdfBD?1MLEw1?1Bsgy8wGdfMLej? AUB K G MzdfBDC|CxB AmwU?1B e!?1AUBA1B FGJIKLBgMzN!OsDdoG]MLBg?5d2KLBgC sDyw1G]dfMze!?1C_ej?1AGj&Bg?5doG]KLBgC Cxw1Mz]Gj?5d|BgC /:+;=<!;bR U (0) · K U (0) = 0, e BgCdKzB{1KLenEML?UsD|MzBgw1°N5G]w1noO1BA1BHKLGpG]d||MzngB N T n s4doGj?5d¢w1?&Bg?5dfMzBg

(63) +GjMz?1C|M K T TZBDd|nj;kmBDCxdkwU||MzB <7Y5WjY{y8w1MG K = N + ρv I K = K N + N

(64) K s4doGjUKLM°ngBDCsgy8wGdfMLej?1C_KzB-rU|Bg&MLBDgT)C|wUMzM¢r1Gj GjtDMLBD <7Y!!Y 4; p nDB}BgKzKLBgCDT DmGjM d||e!w+!s2K/msDy8wG]dfMze!?A1B2KLG+M=dfBDC|C|B_r ejw1HwU?1B_ej?1A1B2AUB2FGJI+KzBgMzN!O A1Gj?1CA1BgCHng|MzCxdfGjw+³ G]?1MLCxejdfxe!r BDC2dfejw1|?G]?8d|C Ph<:+T{<7[]\/T°w1?1B s4dfw1AUB ywUM¢dfxe!wUjB A1BgC~GjrUr1KLMznJG]d|MLe!?1CAGj?UC KLG -MzC|BG]wre!Mz?8d@A1BNjI|e!Cxnge!rBgC&ML?1MLG]dfw1xBgC ¢Gj?1NUT(:ji!i5q ;_vnDM°MLKsDdoG]MzdprG]xdfMzn4u wUKLM D|BD-BD?8d£Mz-re!xdfGj?5d°A1B?1BrGjC£?1sgN!KzMLN!BD KmGjngnDsgKLsDfG]d|MLe!?nDBg?5dfxMzw1NjBHrG]£|Gjr1re!xd }nDBgKLKzBpA1B_ke!|Mze!KLMzCgT8!e!Mz MLNjw1|B:+;b:+; Tˆ = (N3 +ρv 2 I)−1 ,. ˆ = N1 (N3 +ρv 2 I)−1 , R. ˆ = N1 (N3 +ρv 2 I)−1 N

(65) +N2 . Q 1 . . 3. 2. . . . 2. . (n). (n). (1). n. 2. 3. (2). (1). 1. (1). 1.

(66). . . . . #

(67)

(68). .

(69)

(70) !% +(!. ,.

(71). . BDCpe!?1A1BDC@A1B&cd|e!?1BgKzBDI C|BrU|e!rG]N!Bg?5d`} K/mMz?8d|Bg0GjngB_r1K Gj?UB2A1BA1BDw+³Cxe!KLMzA1BgCHsgKLGjCu d|MLy8w1BDC(CxBg&M=u®ML? ?UMLCC|e!w1AUsgCg; .(G{nDe!?1A1M=dfMLej?pGjw+³`nDe!?5dfe!wU|CBgCd(ywUB£KzBgCA1sDr1K G]ngBg&Bg?5d|C KzBgC`dffG]nDdfMze!?1CC|e!MzBg?5d_nge!?5dfMz?8w1C} K/mMz?5dfBg0GjngB ; vngM£?1M¢KLGej|&B* /:+;bi+;mV x = 0 ?UMK G_ej|&B :+;=<!;=< ¢?1BpCxBgUKLBg?5dEe!r+dfML-GjKzBgCre!w1KLBgC{sDy8wG]dfMze!?1ClAUw&e!wUjBg&Bg?5dJ; UmGjM A1e!?1npN!sD?1sg|GjKLMzC|sHKLBgC{sDy8wG]dfMze!?1Cej?1AGj&Bg?5doG]KLBgC :+;=<!;mR¢}KLG2r1|MzC|B@BD?nge!&rUdfB CxMLwUKzdoG]?1sgB@AUBgCA1sgr1KLGjngBD-BD?5dfCEBDdA1BDCd|fGjn4dfMLej?1Cg; °KzKLBgC{Cxe!?5dA1e!?1?1sDBgCrGj :+;b:+;=< ˆ ξ(0) = 0, ξ(0) · IN e ˆ BgCdw1? Bg?5dfMzBgg;.)G r1xBgwUjB BgCdA1BDC2r1Kzw1C2CxML&r1KLBDC-Ph<7iUT :+<!T 0 I BDd I = n klR\; e!w+dHIAZbGj0e!xATXe!? &e!?5dfxB`rGjE|sDngw1x|Bg?UngB2y8w1B N re!C|C gA1B_w1?1BCxd||w1n4dfw1xB <JR

(72). 2. n. n. .

(73) :+;X>@?1A1BDCHKzML?1sgGjMLxBgCBD? sDK GjCdfMzngMzd|s@KLMz?1sJG]ML|B. V ite s s e d e l’o n d e d e R a y le ig h (m /s ). 34 00. x1. x. 335 0. 3300. 325 0. Ω 3 x2. 3200 0. 0.02. 0.04. 0.06. 0.08. 0.1. 0.1 2. 0.1 4. t a u x d e r o t a t io n / p u ls a t io n. LM N!wU|B~:+;b: >@?1A1B~A1B&FGJI+KzBgMzN!OC|w1`KLG C|w10GjngB~ASw1?C|e!KzMLA1B C|MLKzMLnDB BD?©xejdoGdfMLej? P=<:TZ<7[]\/; 0A1xe!Mzd|Be!? je!MzdlK G]GjxM G]d|MLe!?-A1BpK G+M=dfBDC|C|B`GJjBgnpKLBfGjr1re!d e Ω BgCxd¢KLB{dfGjw+³&A1B|ejdfG]dfMze!?~BDd ω KLG`rUw1KLC|G]dfMze!?T5Bg?&dfBD?Gj?5dnDe!&rUdfBA1BEdfe!w1C£Ω/ω KLBDC°dfBgx-BDC |ejdfG]dfMze!?1?1BDKLC d|fGjM=dsDrGjMLC"£B4dlBg??1sgN!KzMLN!BgGj?5dK/bG]ngngsDKLsDfG]d|MLe!?&ngBD?8d||M=w1N!B 6dffG]Mzd ? ; c+Me!?-BDC|w1xB`w1?1B`+M=dfBDC|C|BA1BR!R5q]i~ 2]C 6dffG]MzdfCr e!Mz?5dfMLKzKLsDC4Te!?r BDwUdC|B`dfxe!-rBg A1B`V8q µA1Gj?1CEK GA1sDA1w1nDd|MLe!?A1wfG]r1r ejxdP doGjw+³ A1B`|ejdfG]dfMze!?U\ 2UPSrUw1KLC|G]dfMze!?U\/; C|ML&MLKLGjMLxB}&nDBgKLKzB@A1B N Tn]mBDCxdu }u®A1MLxB " # /:+;b:+; : N N N = , . .

(74). (n) 1 (n). n. K. (n) 2 (n) N1

(75). e K BDd N C|e!?5dCxI-s4dfxMLy8w1BgCD;HvK(CgSBg?Cxw1MzdHy8w1B IN BDCxd r e!wU ˆ dfe!wUd n ;°²°w1MLC e!?&r1xBg?1A&KLB{r1xe+AUw1Mzd CxnJGjKLGjMLxBlA1BKSsgy8wG]d|MLe!?A1w&&e!wU!BD-BD?5d /:+;miU;bY rGj IN e!? G xe!wUdfB_}-nDBDdxdfB2sDy8wG]dfMze!? ˆ ξ BDdHe!? e!UdfMzBg?5d ξ · IN ˆ ξ = M ξ · IN ˆ ξ C|e!?nge!&r1KzB4³+Bpnge!? xw1N!w1s`re!w1 ?1MzEGJ!Bgn :+;b:+;mR ˆ ξ + ξ · IN ˆ ξ = 0, ξ · IN BDdJTZrGj@Mz?8d|sgN!|G]dfMze!? BD?8d||BK/mMz?8d|Bg0GjngB x = 0 BDdpK/mMz? ?1M 0e U BDd t TB4dÀ1e!?1n ξ T A1MLCxrGjfG]MLC|CxBg?5d Te!?Gj|xMz!B } /:+; :;z< o;²ªGjB ³UBD-rUKLBjTre!w1w1?UB£ej?1A1B°A1B£FG7IKzBgMLNjOpe!? G@K GnDe!?1A1M=dfMLej?Gjw+³nge!?5dfejw1|C ξ(0) = [U (0), 0]

(76) T!B4d KLBDC°sgy8wG]d|MLe!?1Ce!?1AGj&Bg?5dfGjKLBDC :+;b:+;=< C|B`|sDA1w1MzC|Bg?5dH} :+;=<!;mR ; °? wUdfMzKLMLC|Gj?5d :; :+;=< oTe!?r BDwUd|sgCxe!w1A1xB2BD?8d|M D|Bg&Bg?5dKLB`r1xe!1K g&BpA1BgCe!?1A1BDC A1Bc8dfe!?1BDKLB4I A1Gj?1Cw1? 1Mhuv-G]dfsD|M G]w r e!wUHKzBgy8w1BgK)KzBgCA1Bgw+³ A1BD-MhuvBDC|rGjnDBgCHC|e!?5dHe+n u ngw1rsgC)rGjKzB ,g&B C|e!KzMLA1B]T7G]MLCnoOG]ngw1?_GJ!Bgn£w1?1B G]?1MLCxejdfxe!r1MLBªywUM!BgCdCI-s4df|Mzy8w1B <JV (n). (n) 2. . n. n. n. 0. . . n+1.

(77). 0. n 0. n.

(78). 2. . . .

(79) :;>p?UA1BgCEKLMz?1sJG]ML|BDClBg?sgKLGjCxd|MLnDMzdfsKLML?UsJGjMz|B 180 o. X x1. x1. X. X. Y. X. Y. x2. LM N!w1xB`:+;mR £>@?1A1BÀ1Bcd|e!?1BDKLBDI }KSML?5dfBDx0GjnDBpAmwU?UM=uv-G]d|sg|MLGjwCI-s4df|Mzy8w1B&P=<7i\ rU|eA1w1nDd|MLe!?ASw1?G]ngKLB@}&rG]xdfMzlASw1?ng|MzCxdfGjKe!dfO1e!xO1e!UMLy8w1Bj; r1Gj{fGjrUr e!d}&K/mMz?5dfBg0GjngB Ph<7i]\/; . SMLAUsgBpC|ejw1Cu |GjngBD?8d|B_MzngMBDCxdHA1B`-eA1sDKLMLCxBg KzBgC{nD|MLCdoGjw³G]ngKLsDCgTUje!ML xMLN!=w1xB0 :+;mRU;

(80) G]?1C KLBgC GjwUdfxBgC°ngGjC 0CxM1KLBDC°A1Bgw+³A1Bg&M=u®BgC|r1GjngBDC C|e!?5d£engngwUr sDC°rGj°A1BDC°G]d|sgxM=u G]w+³-A1M sgxBg?5dfC"4TUKzBgC£sgy8wG]d|MLe!?UC£e!?UAGj&Bg?5doGjKzBgC£?1BCxe!?5dlr1Kzw1CngGjrGjUKLBgC£A1BHN!sg?1sD|BD K/msDy8wG]dfMze!?A1B2KLG&Mzd|BgC|CxBj;H²e!wUKLBDCe!?UA1BgCHA1Bcd|e!?1BDKLBDIre!K G]|MLCxsgBDCHAG]?1Cw1?r1K Gj? AUB©CI+&sDd||MzBnDe!&w1? Gjw+³ A1BDw+³ C|e!KzMLA1BDCgT@ej? rBgwUd-GjKLNj|s dfejwUd©Pb:j[\pdf|ejwU!BD K/msDy8wG]dfMze!?B4³UGjnDd|B A1B-K G +M=dfBDC|C|B* :+;miU;=<!< pBDd_sgKzw1ngMzA1BgKLB&r1|ej1K D-B]T(je!ML MLNjw1|B :;mV1;ª²e!wU£nDBgKLG`MzK1?1B{0GjwUd r1GjC O1sgCxMzdfBD£}`xsgCxe!w1A1xBHG]?GjKzI8d|MLy8w1Bg&Bg?5d KzBgC°A1BDw+³&y8wGju d|MLy8w1BDCA1B¢kO1|MzCxdfe ZBDKT7w1?1B°d noO1B y8w1M!C|B xsD DKLB,Dd||B sDd|e!?1?G]-&Bg?5dCxML&r1KLB]; .)BDC)1M=u -G]d|sg|MLGjw+³ C|e!?5dwUdfMzKLMzC|sgC{Mz?5dfBg?UC|MzjBg&Bg?5dHAGj?1CKSML?1AUw1Cxd||MLBA1BgCC|BD-Mhuvngej?1A1w1n4dfBgwU|CgT Nj nDB2Gjwr1xe+nDsgA1sA1B ngejKLKLBpC|Gj?1Cnge!KzKL B oT1y8w1M(r BD|&BDdA1BKLMzBg{A1BG]?1M D|BprBg|-Gu ?UBg?5dfBHBDdlxMLN!MzA1B{A1BDw+³ nD|MzCxdoG]w+³&Bg?-KLBgC£re!KLMzC|CfG]?8d£CxM 1MzBg?-ywZmMzKLC CgmG]d|dfGjnoO1BD?8dlrGj£KLBgC ej|ngBDCEA1BpjG]? A1BD ¤GjKzKLCD; . . . 2. . . . . #

(81)

(82)

(83) , . . . . BDC&ej?1A1BgCAUBcnoO1e!Kzd|B C|B r1xe!rGjNjBg?5d&}KSML?5dfBDx0GjnDB ASw1? A1Bg&M=u®BgC|r1GjngB Cxe!KLMzA1B BDd AZmw1? A1Bg&M=u®BgCxrGjngB`BD-r1KzMASw1?¡w1MLAUBr1Gjx0GjM=dJ; °KLKzBgC{C|ej?8ddf gCEr1xsgC|BD?5dfBgCBg?N!sge]u rUO8ICxMLy8w1B2B4dBg? d|BgnoO1?Ue!KLe!NjMLBpA1BDCHngGjrUdfBDw1|CD;lvngMKLGnge!?1AUMzdfMze!?Gjw+³KzML&MzdfBDCBDCxdHywUB KLGnge!&r ejCfGj?5dfB?1ej|-GjKLB A1w A1sgrUK GjnDBg&Bg?5d&BDd-A1B KLGnge!?5df|GjML?5d|BBDCxd-nge!?5d|ML?8w1B } d|fGJ!BD|CKSML?5dfBDx0GjnDBjTUdfGj?1A1MzC{y8w1B`K Gnge!?5d|fGjMz?8d|BpA1B`ngMzCfGjMzKLKLBD-BD?5dlCg IGj?1?8w1KzBj; °?wUd|MLKLMzCfGj?5dKLBDCHsDy8wG]dfMze!?1Ce!?1AGj&Bg?5dfGjKLBDC :; :+;=< {e!? rBgwUd|sDC|e!w1AU|B Ph<7R]\(KLB rU|e!1K g&BEAmwU?1Be!?UA1BHAUB@c+noOUe!Kzd|BHre!K G]|MLCxsgB{AG]?1Cw1?-r1K G]?-A1BCxI&sDd||MLBA1w-C|e!KzMLA1B B4d|BgrU|eA1w1MLxBpA1BgCEA1ej?1?1sgBDCHB ³+r sD|ML&Bg?5dfGjKLBDC{e!UdfBD?8w1BgCrGjEAmGjwUd||BgCDT1!e!Mz MLNjw1|B :; q+; <7q. . . .

(84) :+;X>@?1A1BDCHKzML?1sgGjMLxBgCBD? sDK GjCdfMzngMzd|s@KLMz?1sJG]ML|B v (km/s) 1.5. Rayleigh. Y∗. PSfrag replacements. Stoneley. 1.45. C ρ . X∗. x 3 ρ∗ ∗ Cij. θ∗. 1.4. x1. θ. ij. 1.35. X Y. θ 20. x2. 60. 40. 80. LM N!wU|B~:+;SV >@?1A1B~A1B-cd|e!?1BDKLBDI}K/mMz?5dfBg0GjngBAUB&AUBgw+³QCxe!KLMzA1BgC`G]?1MLCxejdfxe!r BDC 0r1Mz?

(85) e!w1N!KLGjC 2 0ngGj|e!?1BBDr eJ³I Pb:j[\; .)G MLN!wU|BA1B~A1xe!Mzd|B|BDr1|sDC|Bg?5d|BK G]GjxM G]d|MLe!? A1B`K GMzdfBDC|CxB 6df|GjMzdEsDrGjMLC"lGJ!Bgn_KmGj?1N!KzB@A1B`ngejw1r B θ A1wnJGjx ej?1B`Bgre7³Ij; .°mGj?1N!KzB A1Bnge!wUr BA1wQr1Mz?

(86) e!w1NjK GjC@BDCxd U³+s~} θ = 0 ;2>p?je!Mzdpy8w1BK/mej?1A1BA1B&c8dfe!?1BDKLB4I ?mB ³+MLCxd|By8w1B~r e!wU ; .BDCpnge!w1x BDC`Bg?QdffG]Mzd 1?xBgr1xsgCxBg?5dfBD?8d2KLBDC jG]|M GdfMLej?1CA1B`K/me!?UA173BpA1B<FHθGJI<KLBDML107 N!Ore!w1{noOG]ywUB_Cxe!KLMzA1Bpr1|MzC{C|sDrGj|sD-BD?5dJ; . .

(87). ∗. ◦.

(88). ◦. x 1. θ X. v ite s s e d e l’o n d e d e S c h o lte [m /s ]. 28 00. 26 00. 24 00. 2200. 2000. Y. 20. x2. 4 0. 6 0. a n g le d e c o u p e [ d e g ]. 8 0. LM N!wU|B:+; q >@?1AUBA1BcnoO1e!Kzd|B }K/mMz?8d|Bg0GjngB&ASw1? C|e!KzMLA1B 0NjBg|-Gj?1Mzw1 pB4dASw1? ¡w1MLAUB nge!?UC|MLAUsg|s r1Gjx0GjM=d -B4dfOGj?Ue!K)~P=<JR]\; .)G MLNjw1|B-A1B A1|ejMzdfB-|BDr1|sDC|Bg?5d|B KLG jG]|M GdfMLej?A1BK G@MzdfBDC|CxBGJ!BDnHK/bG]?1N!KLBA1BHnDe!w1rBEA1wN!BD|-Gj?1Mzw1 T]KLe!xC|y8w1BK GMzd|BgCxC|B A1w C|ej? AGj?1CHKLB-s4dfOG]?1e!K)BgCd 0 2]C" E:jiji!i* nge!w1x B_A1w G]C4T R!i!ijiUTR5qji!iUTV5i!iji 0ngejw1|BA1w O1GjwUd ; ² Kzw1CK Gr1xBgCxC|MLej? BDd&A1e!?1nKLGM=dfBgCxC|BA1w C|e!?&~G]w1N!&Bg?5dfB]T r1KLw1C-KSB+ BDdA1B KmGj?1MzC|ejd||e!rUMLBBgCd G]|y8w1sjT{BD? GjngnDe!|A GJjBgnKLBDCB ³UrsgxMLBD?1ngBDC A1B k|e EO8w1|CdB4dG]K; /:ji!iU< ; <7[ . . .

(89) :;>p?UA1BgCEKLMz?1sJG]ML|BDClBg?sgKLGjCxd|MLnDMzdfsKLML?UsJGjMz|B " #

(90) #

(91)

(92) $ !% ! ! * , .BDC&Mz?1Cxd||w1&Bg?5d|C~}d|fGj?UC|A1w1n4dfBDw1|C-Amej?1A1BgC~A1BCxw1x0GjnDBr1MLsDtge]uvGjnge!wUCxdfMzy8w1BgCCxe!?5d Mz?1?1e!21fGjUKLBgCDTlC|wUxdfejwUd AG]?1CK/mMz?1A1w1Cdf|MzB AUBK Gnge!&w1?UMLnJGdfMLej? C|Gj?1C 1K 6dfsgKzs4u rUO1e!?1B-r e!doGjUKLBjTCxICxd g&B A1B-r e!CxMzd|MLe!?1?UBg&Bg?5d2NjKLe!G]KTdfsDKLsDMzC|MLej? ngejw1KLBDw1gTnJGjr+u d|Bgw1xCgTEBDd|nj; ae MLKzC-Cxe!?5d wUd|MLKLMzC|sDC&nDe!&-B Kzd||BDC-OG]wUdfBDC|sDywUBg?1nDBgC /FEe7I!BD

(93) MLBgwUKLBgC|GjML?5dgT(:ji!i!i ; .Bngejw1r1K G]N!BA1B~KSsgKLGjCxd|MLnDMzdfs2GJ!Bgn~KLG r1MLsDtge]u®sgKLBDnDd||MLnDMzd|s2ngej~u rUKLMLy8w1B@ejxdfBD-BD?5dHKzB`r1|e!UK g&BpA1B`K Gr1xe!rGjN!G]dfMze!? A1BgCe!?1AUBgCAmMz?5dfBg0GjngB]TX ,D-B A1Gj?1CKLB&nJGjA1xB-AUB-K/bGjrUr1|eJ³+ML-G]dfMze!?y8wGjCxM=uvCdoG]d|MLy8w1B]; °? rGjdfMzngw1KzMLBgDT)K G Gdf|MzngB AUB`cdfxe!O rG]C|C|BpAUB@K G`doGjMzKLKLB }KLGdfGjMLKzKLB ; kBgrBg?UAGj?5dJTe!?r BDwUd{wUd|MLKLMzC|BD KzBgC{sDyw1G]dfMze!?1C{e!?1AG]-BD?8dfGjKLBD6C{×r ej6w1{|sDC|e!w1AU|B8ng×Bg8doGjMz?1CEnJGjCEASe!?1AUBgCEASML?5dfBDx0GjnDBj; 0HML?1CxMTre!w1pK/me!?UA1BA1B KzBgw1CdfBgMz?+u pw1K=I5GjB4 r e!KLGj|MzCfG]d|MLe!? O1e!xMLtgej?8dfGjKLBdf|Gj?1Cu jBgxC|B TpKSsgy8wG]d|MLe!? A1B©kO1xMLCdfe BgK@CxB0G]nDdfej|MLCxB Bg?5d|M gxBg&Bg?5dr ejw1K G¤CxI&sDd||MLB []- 0BDd£K/msDyw1G]dfMze!?~A1BEK G@MzdfBDC|CxBHnDe!|xBgC|re!?1A1Gj?5dfBBgCxd¢KLMz?1sJG]ML|B¢Bg? ρv G]KLe!xC°ywUB re!w1HKLBDCCxI&sDd||MLBDC T T TZ:jRUTnjSBgCd`w1?1By8wG]xdfMzy8w1Bj; d|e!?1?Gj&&Bg?5dJT e!? d||e!w+!B Ph<W\y8w1BAGj?1¯4Cng¯42BA1BD|¯43?1MzBgHnJGjCDTKSsgy8wG]d|MLe!?A1B2KLG-MzdfBDC|CxBr ejw1A1BDCpnge!?UA1M=u d|MLe!?UC¢G]w+³&KLMz-M=dfBgCª-s4doGjKzKLMLCxsgBDC°BgCxdw1?1B BD? ρv ; kBxsgCxw1KzdfG]d£A1BgC¢r1KLw1C CxML&r1KLBDCgT8y8wSe!??1Bre!wU]GjMzd£rG]C¢A1B4ML?1BD}KmG7]Gj?UngBjT8BDCxd0G]ngMLKzBg&Bg?5d e!Ud|Bg?8w N! ngB G]w+³ sgy8wG]d|MLe!?UC&e!?UAGj&Bg?5doGjKzBgCD;²ejw1-wU?1B Cxw1x0G]ngB?Ue!?+uv&sDdfGjKLKzMLCxsgBjT°ej? dfxe!wUjB wU?1B`C|B4³d|MLy8w1BBg? ; ?1BejMLC{K G2M=dfBgCxC|B`dfxe!wU!sDBjTXK GA1BDC|nD|MLr+dfMLej?nDe!&r1K 4dfBpA1BDC noO1Gj-rUCBD? AUsgngejw1ρvKLB]T1!e!Mz MLN!wU|B`:+;m[U; >@? rBgwUd{Gjw1C|CxMd||e!w+!BgA1BgClxsgCxw1KzdfG]dfC¢B4³+r1KLMzngM=dfBgC£re!w1KzBgC¢e!?1A1BDClr1MLsDtge]uvGjngejw1Cu d|MLy8w1BDC{A1B`C|w10GjngB}A1BDw+³ngej-re!CfG]?8d|BgCPm:!q\B4dr e!wUlKLBDC{e!?1A1BDCEd|fGj?UCx!BD|CxBgCO1e!u Mztge!?5dfGjKLBDC{AGj?1CEKLBDC{Cxd||w1n4dfw1xBgCnDe!w1noO1B 2]C|wU1Cxd|fG]d2PmRjiUTXk{q\ e!?1A1BDCAUB .e7!B 4; #

(94) #

(95)

(96)

(97)

(98) &(!% ,

(99) Gj?1CK/mMz?1A1w1Cdf|MzB-AUBgCCxBg&M=uvnDe!?1A1wUnDdfBDw1|CDT A1BDC2dfBDnoO1?1MLy8w1BDC~GJjG]?1ngsDBgCrBgx-B4d|dfBD?5d K/msDK Gje!|G]dfMze!? A1BGdfsgxM Gjw³}~N!fGjAUMLBg?5dA1Br1|ejr1|MzsDdfsDCg; 0ML?UC|Me!? r BDwUdML-GjN!ML?UBg y8w1BHr ejw1¢wU? C|w1UCxdf|G]d x ≥ 0 T8K G`|MzN!MLAUMzdfs c T+KLGnDe!?1CdoGj?5dfBHr1MLsDtge]u®sgKzBgnDd||MzywUB e T KLGngej?1CxdfGj?5dfB{A1MzsgKLBDnDd||MLy8w1B T!B4d K GH-GjCxC|Bl!ejKLw1&MLy8w1B ρ jG]|MLBD?5dªdfejw1C A1B{KLG ,D-B -Gj?1M gxBpGJ!BgnK Gr1xeje!?1AUBgw1 :; q+;=< {c (x ), e (x ), (x ), ρ(x )} = {c , e , , ρ }f (x ), e T T T C|e!?5d@AUBgCpngej?1CxdfGj?5dfBgCDTBDd f BgCdpK G

(100) $

(101) $ )

(102)

(103) ! ( c e ρ e!?re!CxB ;EkBDdxdfBO5I+rejd|O gCxBBgCd1MzBg? C 1MLx|sJG]KLMLCdfB@-GjMzCBDKLKzBpr BD|&BDd AUB¢0GjMz|B A1BgfC(0)r1|ej=N! 1DC Gj?G]KzI8dfMzywUBgCgT]y8w1M+re!w1x|e!?5dC|BDxML(ASsDdoG]KLe!?+u®|s4sg|BD?1ngB¢KLe!xCAUw r1GjC|C|GjN!B@}_A1BgC¢ML?1O1ej-e!Njsg?1sDMzdfsDC r1KLw1C¢nge!&r1KzMLy8w1sgBDCg; vKGjrUrGjfGLd£y8w1B@KLBDC£ej?1nDd|MLe!?1C <7W . . .

(104).

(105). .

(106). . .

(107). . 2. . . 2. . 2. . . . . 2. . 44. ◦ 44. 44. 11. ◦ 15. 2. 15. ◦ 11. ◦. 2. 11. . 2. 2. ◦ 44. ◦ 15. ◦ 11. . . . 15. ◦. 2. . .

(108) :+;X>@?1A1BDCHKzML?1sgGjMLxBgCBD? sDK GjCdfMzngMzd|s@KLMz?1sJG]ML|B 1760. f = 100 MHz, λ =17.5572 µm,. 1. x 10. u (m). 1740. 12. 10 10 8 6 0. 3. 0. 5. x2/λ. 5 0 0. −10. −10. VB G m. −1. 0. 100. 200. 1720. 300. 400. −15. 500. −15. −4. 100. 4. (V). 1690. φ (V). VAC. φ 0 −5. 0. 0.5. B G f. 0 −10. −8. −6. −4. −2. −3. 0. 0. 100. 6. 500. 4. 50. 60. 70. 80. D (C/m ). 2. −9. −0.4. x 10. D (C/m2). vacuum 2. 2. 0. D. 2. 0. 2. 2. (C/m ). 4. 2 VAC. −0.6. −2 −5. −0.8. 40. x 10. 2. (C/m ). 48. D. 44 46 θ (d e g .). 2 VAC. 42. 300. x2/λ −9. x 10. −0.2. 1745. 30. 0. x2/λ. 1680. 20. 400. −2. −9. 10. 500. 0 −1. 5. 2. 1750. 0. 400. 1. φ (V). (V). vacuum 2. x /λ. V. 1670. 200. 4. 1.5 1. 1755. 500. x 10. 2. x 10. 2. VAC. 1700. 5. 400. 3 −4. 1760. 0. −4. x 10. 2.5. 1710. x /λ. 200 300 x2/λ. 2. 0. x2/λ 3. 1660. −5. −5. −0.5. φ. v it e s s e d e p h a s e (m/ s ). 15. −14. x 10. Bi12GeO20 0.5. 1730. θ = 42° 30’, free surface. −13. B u lk. σ32 (N/m2). V. 2. (B G O ). B G f. 32. V. σ (N/m ). 20. u3 (m). B i 12 G e O. 1750. 0. −2. 5. x2/λ. 90. −1 −10. θ (d e g .). −8. −6. −4. −2. −4. 0. 0. 100. 200. x2/λ. 300. x /λ. MLN!wU|Bp:;b[ °>p?UA1BpA1B KzBgw1CdfBDML?+u `w1K=I5GjB4re!w1KSe7³IA1B@AUBp1MLCxwUdfO NjBg|-Gj?1Mzw1 =P <7R\;1.)G MLN!wU|BEA1BN!Gjw1noO1BH|BgrU|sgCxBg?5dfBpKLG`]GjxM G]d|MLe!?~A1BHK GpMzdfBDC|CxBpGJ!BgnHKmGj?1N!KzBEA1B nge!w1rBj;£kBDKLKzBHA1BA1|e!M=dfB-ej?8d||BKLBDC¢]Gj|MLG]dfMze!?1C A1BDClnoOGj&r1C/ A1sgr1KLGjngBD-BD?5ddf|Gj?1C u !BgxC|B]T¢nDe!?5dffG]ML?5dfB-A1B ngMzCfGjMzKLKLBD-BD?5dJT(r ejd|Bg?5dfMzBgK¢sgKLBDnDd||MLy8w1B]T°ML?1AUw1nDd|MLe!?¤sDKLBDnDdfxMLy8w1B G7jBgnKLGr1xeje!?1A1BDw1gT KLe!xC|y8w1B_K G-Cxw1x0G]ngBBgCdp?1e!?uv&sDdoG]KLKLMzC|sDBpBDdpK/bGj?UN!KLBÀ1BnDe!w1rB BgCxd 42 30 ; AmMz?1O1e!&e!N!sD?1sgM=dfs@Cxw1Mz]Gj?5d|BgCEr ejw1 f T cosh (βx + δ) cos (βx + δ) /:+;bq+; : exp(2βx ), (βx + 1) , , , cosh δ sinh δ GjML?1CxM ywUBKLBDw1ML?5!BD|C|B]T°r BD|&BDdxdfBg?5d2w1?1BxsgCxe!KLwUd|MLe!?©nge!&r1K DdfB&A1w©r1|e!UK g&B&A1B KSe!?1A1B{A1B KzBgw1CdfBgMz?+u pw1K=I5GjB4Bg?&CxI&sDd||MLB[j&;

(109) BDC¢&sDd|O1eA1BgC C|ej?8d£r1xe!re!C|sDBgC r e!wU{r BD|&BDd|d||BpA1B`N!sD?1sgxBgAmGjwUdfxBgCEr1xe KLCDT1ngej-&BprGj{B ³UBD-rUKLB tanh (βx + δ) /:+;bq+;bR f (x ) = , tanh δ ywUMEG KmG7]Gj?5dfGjN!B C|wUKLBgCrU|sgnDsgA1BD?5dfBgC-A1B?1B |Gj-GjMLCdfBg?UA1|B !BD|C&tgsD|eQe!w !BD|C KSML? ?UM; °KzKLBAUsgngxMzd{wU?-G]d|sg|MLGjw A1ej?8dEKzBgClr1GjfGj Dd||BDC c (x ) T e (x ) T (x ) T noOGj?1NjBg?5dAZmw1?UB]GjKzBgw1 Mz?1Mzd|M GjKzB c T e T T ρ } KSML?5dfBDx0GjnDB x = 0 ρ(x ) } w1?1B ]GjKzBgw1GjCxI&rUdfe]dfMLy8w1B T T T T_e BDCxdw1? rGjfG] 4df|BG xwUCxdoG]1KLB];{vngMTXKzBr1{cGjfGj Ded||B β rBgwUρd}/Gjw1tanh CxC|M ,DdfxδBG xwUCxdfδs_r >ejw10EA1sgnD|MLxB Gjw1C|CxMZ1MzBg? w1?UB]Gj|MLG]dfMze!?-KzBg?5dfBA1BgC{r1xe!r1xMLsDd|sgCG7jBgnpKLG2r1|e]e!?1A1BDw1gT+ywZmw1?UB@jG]|M=u G]dfMze!? |Gjr1MzA1B`ywUMnDe!? ?1BDfGjM=dK/mMz?1O1e!&e!N!sD?1sgM=dfspAG]?1CHwU?1B2nDe!w1noO1B 1?1B2r1 gCHA1B2KLG C|w10GjngB]; . SML?+¡w1Bg?UngBA1BnoOGjy8w1Br1|e K{C|w1KLGr1|e!r1GjN5G]d|MLe!?¤AUBK/mej?1A1B BgCd~df DC Gjxy8w1sgB]TBDdErBg|&BDdA1B`&e+AUM BDlC|BDCngGjfG]nDdfsD|MzCxdfMzy8w1BgC}!e!Kze!?5dfsj; <7 . . . ◦. 2.

(110). 0. 2. 2. 2. 2. 2 2. 2. 2 2. . . .

(111).

(112). 2. 2. . 2 2 .

(113). . 2. . ◦ ◦ 44 15. .

(114). ◦ 44 ◦ 11. ◦ 15 ◦. ◦ 11. 44 ◦. 2. 15.

(115). 11. 2. 2. 2. .

(116).

(117). 2. . .

(118) : ;>p?UA1BgCEKLMz?1sJG]ML|BDClBg?sgKLGjCxd|MLnDMzdfsKLML?UsJGjMz|B

(119) B-0G#ge!? C|ML&MLKLGjMLxBjT xB--B-C|w1MzC2ML?5d|sg|BDC|Cxs }K Gr1|ejrGjN5G]d|MLe!?ASw1?1B ej?1A1BAUB FGJIKLBgMzN!O A1Bgw³ngej-re!CfG]?8d|BgC"HAGj?1Cw1?A1Bg&M=u®BgCxrGjngB2Gjw+³ ]Gj|MLG]dfMze!?1CEB4³+re!?1Bg?u d|MLBDKLKLBDCgTZG7jBgn~re!w1@e! xBgnDd|Mz£A1B&e+AUsgKLMzC|BDKLBDC@e!?1AUBgC`C|MzC|&MLy8w1BgCAGj?1CpKzBgC@&MLKzMLBgw³ Cdf|G]dfM sgC¢PmR!:\;vngM+Gjw1CxC|MKSML?1O1ej-e!Njsg?1sDMzdfs xejw1B¢wU? KzB¢rU|sgre!?1AUsgfG]?8dg; °?rG]xdfMzn4u wUKLMLBDgT!BDKLKzBlML?5dfxe+AUw1MzdªA1B{K G@A1MzC|rBgxC|MLej?r e!wU°KLBgC°ej?1A1BgC A1BEFGJIKLBgMzN!O 0y8w1MCxe!?5d ?1e!?+u AUMLC|rBgxC|M=!BgC(Bg?_-MzKLMzBgwpO1e!&e!N D?1B TBgKLKzB A1MLCdfML?UN!w1B°KLB nDe+B -nDMLBD?8dAmG]d|d|sg?8wG]d|MLe!?A1BDC AUsgr1KLGjngBD-BD?8d|CHAUBnDBgw+³ A1BDCd|fGjn4dfMze!?1CgTB4dBgKLKzBpr BDwUdEe!|nDBgKmGj&r1KLM=dfw1A1B}&ejC|ngMzKLKzBg BD? AUsgngxe!MLCxCfGj?5dHGJ!BDn_KLG~rU|eje!?UA1Bgw1D; . .

(120). . . . . <JY.

(121) :+;X>@?1A1BDCHKzML?1sgGjMLxBgCBD? sDK GjCdfMzngMzd|s@KLMz?1sJG]ML|B. :ji.

(122) . . . & . °?~sgKLGjCxd|MLnDMzdfs¢0GjML1KzBg&Bg?5d ?Ue!?+uvKzML?1sgGjMLxBjTe!?~r ejw1C|CxBKzBgC°A1s4!BDKLe!r1rBg&Bg?5d|C£AUBgC sgy8wGu d|MLe!?UCE}~K/mej|A1xB@C|e!wUOGjMzd|sjTB4dEe!??1sgN!KzMLN!BKLBgCld|Bgx-BDCCxw1Mz]Gj?5d|Cg; °? ' $ (

(123) $&% ' )! ) r1xe!r1xBg&Bg?5d2AUMzdfB]Tej?©?1B&?1sDN!KLMzN!B~Gjw1nDw1? dfBD|&Bj; e!w+dfBgC_KLBDCNjfGj?1AUBgw1xC Cxe!?5d°ngej?1C|BDx!sDBgC BDdªKLBDC sgy8wG]d|MLe!?UCªA1w&e!wUjBg&Bg?5d°Cxe!?5d°A1Mzd|BgCB4³UGjnDd|BgCD; ?2N!sg?1sDfGjK MzK!CgmGjN!M=d)A1B£CxICxd g&BgCªAZmsDyw1G]dfMze!?1C(Gjw+³ÀUsg|M=!sDBgCªr1Gjxd|MLBgKzKLBDC?1e!?+u®KLMz?1sJGjMz|BDCnge!wUr1KLsDBgCg; cMe!?~CgSML?5dfsD|BgCxC|B}`wU?--G]dfsD|MLGjwA1e!?1?Us M;SBj;ªwU?1BEKLe!M1AUBnDe!&r e!dfBD-BD?8d AUe!?1?1sDB 4T ej?rBgw+dErGjxejMLCd||e!wUjBg{A1BDCEC|e!KzwUdfMze!?1ClB ³1G]nDdfBDCgT!ejMLEkOG]r1Mzd||Bq+;£c+MZe!?noO1BgxnoO1B AUBgC A1s4e!|-G]d|MLe!?1C)e!w_A1BgCª-e!w+!Bg&Bg?5d|C y8w1M+B ³+MLCxd|Bg?5d°re!w1)dfe!wUCªKLBDCª-G]dfsD|MLGjw+³ T]ej? ?UBd||e!wUjBy8w1BHKLBgC A1s4e!|-G]d|MLe!?1C°OUe!-ejN g?1BDC ngBDKLKLBDC¢y8w1MXe!?5d¢w1?NjfGjA1MzBg?5d£A1BgC¢A1s4u ej|-G]dfMze!?1C}@nge!&r ejCfGj?5dfBDC ngej?1CxdfGj?5dfBgC"4T8ngej-&BK/bG&e!?5dfxs °|Mzn CxBg? <JY5q!q ;°c+M KzBgC£GdfsgxM Gjw³~C|e!?5d )

(124) ' CgSMLKLC ?1BHr BD|&BDdxdfBg?5dywUBA1BDCA1s4e!|-G]dfMze!?1C MzC|enoO1e!xBgC{GjKze!|CMLKZIGnDML?1y0G]-MzKLKLBDC¢AUBAUsDe!xG]d|MLe!?UClr ejC|C|Mz1KLBDCg; vKlI Gw1? A1e!-GjMz?1B e KSe!? rBgwUd&-GjKLNj|s-d|e!wUd~0GjMz|B A1BDC~r1|e!Nj gC~BD? d|e!wUdfB Njsg?1sDfGjKzMzdfs]Tn]mBDCxd nDBgKLwUMHA1B K GdfO1sDe!|MzB AUBgC

(125) ) ; vnDMHej? nDe!?1CxMLA D|BEw1?1BN!fG]?1A1BEA1sDej|-G]dfMze!?O1e!&e!N D?1B{r ejw1 w1?-Cxe!KLMzA1B{ngej-r1xBgCxC|MLUKLB 0ejw CDmMzK)BgCxdML?1nDe!&r1|BDC|C|Mz1KLB]TKSw1?1BA1BgCHngMz?1y A1sDej|-G]dfMze!?1C{re!C|CxML1KzBgC{BDdHe!?I Cxw1rBgu re!CxB{w1?-AUsgr1KLGjngBD-BD?8d AZbGj&r1KzMzdfwUA1BMz? ?1M=dfsgCxML-GjKLB]; 0ML?UC|MUej?-G@d|e!wUd°AmGje!|A~w1?UB NjfGj?1AUBHA1s4e!|-G]d|MLe!?O1ej-e!N g?1BCxdfG]dfMzywUBjT8r ejw1¢KLGjy8w1BgKzKLB{e!?&wUd|MLKLMzC|B{KzBgC£sgy8wG]d|MLe!?1C B ³UGjnDd|BgC A1B KSsgK G]CxdfMzngM=dfs ?1e!?uvKLMz?1sJG]ML|B Er1w1MLC-e!?nDe!?1C|MzA gxBw1? r B4dfMzd-ejwU!BD-BD?8d re!w1KLBgy8w1BDKe!? KzML?1sgGj|MzC|BKLBgCsgy8wG]d|MLe!?1ClGjw !e!MzC|Mz?GjN!B@AUBpK G_NjfGj?1AUBpA1sDe!xGdfMLej?; kBDC{sgy8wG]d|MLe!?UCC|ej?8dE-GjMz?8d|Bg?G]?8d£Bgx-BD-BD?5dlsDdfGj1KzMLBgCDTUN! ngBGjw+³B+ e!xd|ClA1B ¢MLejd <7Y![5q4TX>@N!A1BD? <7Y!]V 4T1B4d BgGjw1ngejw1r AZbGjw+df|BDCg; °KLKzBgC{C|B`KzMLC|BD?5d /R+;biU;=< A u = ρu , e BgCdKLB2d|Bg?1CxBgw1pMz?1CxdfGj?5doGj?1s y8wG]dfxM D-Bej|A1xB HA1BDC`-eA1w1KzBgCAZmsDK GjCdfMLnDMzd|sj; A °?QA1sD?1ejdoG]?8d`r1Gj F KzBN!|GjA1MLBD?5dpA1BK G NjfGj?1AUBA1sDej|-G]dfMze!? CxdfG]dfMzy8w1BjTCxBgC`ngej~u :<. . . . . . . . . . .

(126). . . . 0jilk k,lj. i,tt. . 0.

(127) UR ;X>@?1A1BDCHKzML?1sgGj|MzC|sgBDClBg?sgKLGjCxd|MLnDMzdfs?1e!?+u®KLML?UsJGjMz|B r e!C|Gj?5dfBDCCxe!?5d. 0 RU;miU; : e W = W (F ) BgCdHKLG2A1BD?1C|M=dfspASsg?1BD|N!MzBpA1BÀ1sDej|-G]dfMze!?A1wCxe!KLMzA1Bj;£c+M KLBpCxe!KLMzA1B BgCxdlML?1nDe!-rU|BgCxC|Mz1KLB]T8d|e!wUd|BgClKzBgCAUsDe!xG]d|MLe!?UC£B4dl&e!wUjBg&Bg?5dfClCxe!?5d{MLCxe+noOUe!|BDCgTUnDB ywUMML&r e!CxB@KLBDCEKLM G]MLC|ej?1CMz?8d|Bgx?1BgCEC|wUMz]Gj?5dfBDC A1BDd F = 1, u = 0, /RU;miU;mR BDdnge!?UA1w1MzdH}~KSML?5dfxe+AUw1nDd|MLe!? ASw1? w1Kzd|MLr1KzMLngG]dfBDw1A1B .)GjN!|Gj?1N!B]TC|e!wUjBg?5d@AUsg?1ejd|s ;.BgCEsgy8wGdfMLej?1CEML?1nD|sg&Bg?5dfGjKLBDC{A1w &e!wUjBg&Bg?5dC|e!?5dHGjKze!|C p 0RU;miU;mV A u − p = ρ∂ u /∂t , e p BDCxdKSML?Ung|sD-BD?5dEA1B p ; .BDClsgy8wG]d|MLe!?UCML?Ung|sD-BD?5doGjKzBgCAUw -ejwU!BD-BD?8dle!?5dlngKLGjMLxBg&Bg?5d¢w1?1B@CxML&MLK G]|Mzd|s G7jBgn@nDBgKzKLBgC£A1BHKSsgK G]CxdfMzngM=dfs{KLMz?1sJG]ML|BEG]?1MLCxejdfxe!r B :;biU;=< oTUGJjBgn@y8w1BDKLy8w1BgCA1M sgxBg?1nDBgC G xBDw1|BDCg; °?rG]xdfMzngw1KzMLBDgTjKzBgC &eA1w1KLBDC A A1sgrBg?UA1Bg?5d£A1BlKLGKLe!MA1B{nDe!-re!dfB4u -BD?8d /}Hd|fGJ!BD|C W (BDd AUBlK GrU|s4u®A1sDej|-G]dfMze!? 0}dffGJjBg|C F T!BDd MzKLC(?1B{r ejC|C DA1Bg?5d ywUBKzBgCECxI&sDd||MLBDC{-Mz?1BgwU|BgC 0RU;miU; q A =A , BDd ?1e!? KLBgCCxI&sDd||MLBDCG xBDw1|BDC /:+;miU; : ; vK@I G A1e!?1n©G r1|Mze!|MpV8q &e+A1wUKLBgC AmsDK GjCdfMzngMzd|s-Mz?1A1sDr BD?1AGj?5dfC nge!?5d||B:+< BD? sgK G]CxdfMzngM=dfsKzML?1sgGjMLxB&Gj?1MLCxejdfxe!rB B4d~KLBDC nge!x|BgCxr ej?1AGj?1nDBgC-Bg?5dfxBKLBDC-AUBgw+³ CxICd g&BgC-ASsgy8wG]d|MLe!?1C-?1BC|e!?5d-rGjC-GjwUdfejGu dfMLy8w1BDCg;>@?r BDwUdnDBgrBg?1AG]?8d2|s uvsgnD|Mz|B~KLBDC_sDyw1G]dfMze!?1CC|e!w1C_K G e!|&B~r1|sDnge!?UMLC|sDB rGj`cd||e!OZTBDd`rGj!BD?1ML`} df|Gj?1Cxr e!CxBgpe!w}GjAG]rUdfBDpA1B?1e!U|Bgw³|sDC|w1K=doG]d|CpA1w e!|-GjKLMzC|&BHAUB Gj|?1B4d|du .ejdfOUB4uc8df|ejO; .°SML?5dfsD ,4d)A1BgCxsgC|wUKzdoGdfCe!Ud|Bg?8w1C)MLnDMjxsgC|MzA1B°AGj?UC(KzBgw1xCGjr1rUKLMLngG]dfMze!?1CZ}lK

(128)

(129) $% ' $ ( T2}K/ '

(130) $

(131) $&% A1BgCQCxd||w1n4dfw1xBgCsDK GjCdfe!&sgxMLy8w1BgCBg? N!sg?1MzBgC ngM=MLKUB4d¢GjwUdfej-e!UMLKLB]TjB4d}`KmGjnDe!w1Cxd|MLy8w1B{w1K=df|GjC|e!?Ue!|B{A1BDC£d|MLCxC|w1C 1Mze!KLe!NjMLy8w1BgC -e!wUC¢BD?

(132)

(133) $&%(' )! ) ; .BHr1|BD-MzBg£A1e!-GjML?1Bngej?1ngBD|?1B@KzBgC¢C|e!KzMLA1BDC KLML?UsJGjMz|BgCªr1|s uvngej?8d|fGjMz?5dfCgTBDd¢ngej||BDC|re!?1A}KLG`Cxr sDngMLGjKLMzCfG]d|MLe!?A1BDCsDyw1G]dfMze!?1C ML?1nD|s u -BD?8dfGjKLBDCEA1Bgr1wUMLC vr B4dfM=dE-e!w+!Bg&Bg?5dHC|w1HN!fG]?1A AUsgr1KLGjngBD-BD?8d `!BD|C vr B4dfM=dH&e!w+u !Bg&Bg?5dHC|w1ErBDd|MzdA1sgrUK GjnDBg&Bg?5d f; .BÀ1BDw+³+M g&BA1e!-GjML?1Bnge!?1nDBgx?1B2KzBgC xe!ML?5d|C{Bg? nJGje!w+dfnoO1e!wUnlC|e!wUCªKLBDCªre!?5dfC ejw2C|ejw1C KLBDCªMz-&Bgw1UKLBgC)MzC|e!KzsgC(C|MLCx-Mzy8w1Bg&Bg?5dJT]e!wAG]?1C KLBgCpjsgO1Mzngw1KzBgCgTy8w1M C|e!?5d_C|e!w1&MLC`}A1B&N!fGj?UA1BgCnge!&r1xBgC|CxMLe!?UCg; .B~dfxe!MLCxM g&BA1eu GjMz?1BxBgnDe!w1xdH}KLG2dfO1sDe!|MzBpML?1nD|sg&Bg?5dfGjKLB@ngGjldfejw1C{KLBDCldfMLCxC|w1C{&e!w1C{Cxe!?5dEC|e!wU-MzC }A1BN!|Gj?1A1BDC@nge!?5d|fGjMz?8d|BgCpxsgC|MzA1w1BDKLKLBDCAG]?1CpKLB_nge!xr1C`Gjw xBgre!CgTB4d`} A1BN!|Gj?1A1BDC A1sDe!xGdfMLej?1ClBg?C|BDxMLnDBj; :!: A0jilk = Fjα Flβ. ∂2W , Fiα Fkβ. i,i. 2. ∗ ,i. 0jilk k,lj. i. 2. ∗. . 0jilk. . . 0jilk. 0lkji. . 2. . . . . . . . . . . . .

(134) RU;X>@?1A1BDCHKzML?1sgGj|MzC|sgBDClBg? sgKLGjCxd|MLngM=dfsH?1e!?+u®KLML?UsJGjMz|B

(135)

(136)

(137) . #

(138)

(139)

(140)

(141) !% ! (!' ,. ( . . . .

(142) B?1e!21|BDw+³ r1|ej1K D-BDC&ej?8d-sDd|s xsgCxe!KLw1C&AGj?UCKLBA1ejGjMz?1B A1BDCe!?1AUBgC&ML?1nD|s4u &Bg?5dfGjKLBDCASML?5dfBDx0GjnDBjT+nge!&-BHKSB4³+re!C|BHKmGjxd|MLngKzBEA1B@|B4w1BprGj `w1t :ji!i!: 4T8-GjMLC A1Gj?1CªKzBgw1(y8wGjCxM=u®d|ejdoG]KLMzd|s°MLKzC(Cxe!?5d KzML&MzdfsDC}K/ms4dfw1A1B£A1BDC

(143) $ ) ' TKLej|C|y8w1B KLGAUML|BDnDd|MLe!?A1B&r1|e!r1GjN5G]d|MLe!?QBDd2K G A1Mz|Bgn4dfMze!?©AZbG]dxdfsD?w1G]dfMze!? Cxe!?5dGjKzMLN!?UsgBgCGJ!BDn AUBgw+³©A1BDC_A1Mz|BDnDdfMze!?1C`r1xML?1nDMLrGjKzBgCpA1B&K G N!|Gj?1A1B~r1xs4u®A1sDe!xGdfMLej?; .)GCxd||w1n4dfw1xB AUBgC{sgy8wGdfMLej?1C{BgCdGjKLe!xCCxML&MLK G]ML|B}nDBgKLKzB@A1BDC{sgy8wG]d|MLe!?1C{re!w1w1?1Bpe!?1AUBpBg?sgKLGjCu d|MLnDMzdfs`KzML?1sgGjMLxBpe!xd|O1ejdfxe!rBjTKLe!xC|y8w1BK G~A1MLxBgnDd|MLe!? A1B2rU|e!rG]N5G]dfMze!?BDdK G~A1MLxBgnDd|MLe!? AZbG]dxdfsD?w1G]dfMze!?C|e!?5dHGjKLMzN!?1sDBgCEGJ!BDn_A1BDw+³ G³+BgCEA1B`CI+&sDd||MzBj;

(144) G]?1C¢KzBEnJGjA1xBEA1BgC£e!?1A1BDC¢rU|ML?UngMLr1GjKLBDCgT DmGjM1sDd|w1A1MzsKLGpr1|e!r1GjN5G]d|MLe!?ASw1?1Be!?1AUB G]nge!w1CdfMzywUB}KSML?5d|Bgx0G]ngB2AZmw1?AUBg&M=uvBDC|rG]ngB2BD-rUKLM)ASw1?C|e!KzMLA1B_A1sDej|&s2BDdASw1? AUBg&M=uvBDC|rG]ngBBg&r1KLMEASw1? ¡wUMLA1B+MzC|y8w1BDw+³ ; .)G A1M -nDw1Kzd|s rU|ML?UngMLr1GjKLB MzngM|sgCxMLA1B A1Gj?1C@KLG&xsgngej?1ngMzKLM GdfMLej?TX}KSML?5d|Bgx0G]ngBjTA1BDCnoOGj&r1C .)GjNjfGj?1NjMLBg?UCHwUd|MLKzMLC|sDCHre!w1KLB Cxe!KLMzA1B@GJjBgn`KLBDClnoOGj&r1C °w1KLsD|MzBg?1Clw+dfMLKzMLCxsgCre!w1KLB¡wUMLA1B];.(G&ejd|Mz]G]dfMze!?&A1BpngBDC d|fGJ]Gjw+³ sDdoG]Mzd{A1B@d||e!w+!BgEA1BDC{|sDC|w1K=doG]d|C{r1|sDKLML&ML?1GjMLxBgC£r e!wUlK G&e+AUsgKLMzCfG]d|MLe!?&A1BDC Mz?1Cxd||w1&Bg?5d|C{}2w1K=dffG]C|e!?1CML?5df|Gu®]GjCxngw1KLGjMLxBgC 0ML?5d|Bgx0G]ngB@G]xd D|B/22C|Gj?1N ;.°bGj?1GjKzIC|B &e!?5dfxBy8wmGjw+³OGjwUd|BgCªxsgy8w1Bg?UngBgC wUd|MLKzMLC|sDBgCBg?ML-GjN!BD|MzB£&sgAUMLnJG]KLB dvIr1MLy8w1BD-BD?5d <Ji t 4T KSe!?1A1BBgCd@|Gjr1MLAUBg&Bg?5d@Gd|dfsD?8w1sgBCxw1wU?1Br1xeje!?1A1BDw1ywUMª|BDr1|sDC|BD?8d|B &e!Mz?1CEA1B< 2jqj i

(145) lA1B_KSsgrG]MLC|CxBgw1ASw1?1B2Gjxd g|B]TZB4dy8w1B_KSe!?rBgwUdA1e!?1n?1sDN!KLMzN!Bg KLGnge!wU|1w1xB_B4dKSsgrGjMzC|CxBgw1 ?UMLBpA1B`ngB4d|d|B_A1BD|?1M gxBj;

(146) G]?1C_KzBnJG]A1|B~A1BDC_e!?UA1BgC`?1e!?uvr1xML?1nDMLrGjKzBgCDT DbG]M -MzCpKLBDCpsgy8wG]d|MLe!?1CpAUw©&e!w+u jBg&Bg?5dC|e!wUC_KLGe!|&BA1B-cd||e!OTB4d DbGjMªr1wQ|sgCxe!w1A1xB-AUB?1e!1xBgw+³r1|e!UK g&BgC Nj nDB~Gjw+³QsDyw1G]dfMze!?1Cpe!?1AG]-BD?8dfGjKLBDC :; :+;=< ; 0Mz?1C|M°e!?QrBgwUd`xsgCxe!w1A1xB-BD?8d|M D|B4u &Bg?5dHKLB`r1xe!1K D-BÀSw1?1Be!?1AUB2ML?Ung|sD-BD?5doGjKzB`}-K G~C|wUx0GjnDB_ASw1? C|e!KzMLA1B`C|ejw1-MzC} wU?1B{N!fG]?1A1B{A1s4e!|-G]dfMze!?2d||M=uvG³+M GjKzBjTC|w1M=MLBlASw1?~N!|Gj?1A~ngMzCfGjMzKLKLBD-BD?5dJT!e!Mz MLNjw1|B R+; :+T)Kze!|CxywZmBDKLKLBBDCxd_r ejK GjxMLC|sDBAGj?1Cw1?r1K G]?rU|ML?UngMLr1GjK{Pm:ji]\ 0ej?1A1B-}A1BDw+³ngej~u re!C|Gj?5dfBgC"£e!w&KLej|C|y8wSBgKzKLB{CxBr1xe!rGjN!BEAG]?1C¢?ZmMz-re!xd|B{y8w1BgKzKLBEA1MLxBgn4dfMLej?-ASw1?-r1K Gj? rU|ML?UngMLr1GjK°Pm:jR]\ e!?1A1B_}df|ejMLC{ngej-re!CfG]?8d|BgC"4TXnge!&&B@rGjEB4³+BD-r1KzBÀGj?1CEw1? r1K Gj? AUB_N!|Gj?1AngMzCfGjMzKLKLBD-BD?5dJT+je!ML MzN!w1xB_R+;z<!; 0Mz?1C|M DmGjMr1w Bg?5dfxB2Gjw+df|BDCHxsgCxe!w1A1xB2K G y8w1BDCxd|MLe!?©A1BgCe!?1A1BDC_?Ue!?+uvrU|ML?UngMLr1GjKLBDCpA1BFGJIKLBgMzN!OQAGj?1Cw1?©C|e!KzMLA1BA1B ee!?1B4I8u FEMzKzML? 0C|ejwU!BD?8d@wUdfMzKLMLCxs`r e!wU&e+A1sDKLMzC|BgEKzB_ngGje!wUd|noO1e!w1n HA1sDej|&sjTZwU? r1|ej1K D-B rU|e!re!C|s`rG] K GJML? <7Y![!RB4dE|BDCxdfse!wUjBgdJ; >@? rBgw+dGjw1CxC|M£CgSML?5dfsD|BDC|C|BD} KLG nge!? 1N!w1fGdfMLej? C|wUMz]Gj?5dfB Pb:<g\ 2A1BDw+³©A1Bg&M=u BDC|rG]ngBgCDT¢0GjM=dfCAUw ,g&B -G]dfsD|MLGjw¤O5Ir BD|sgKLGjCxd|MLy8w1B]T¢e!?5ds4dfsC|w xBDdfC&} KLG ,D-B rU|s4u®A1sDej|-G]dfMze!?GJ!BDn&dfGjw+³QA1B~A1MzK G]dfG]dfMze!?rU|ML?UngMLr1Gjw+³ λ T λ T λ T)GJ]Gj?5dA ,4dfxB nDe!KLKzsgC|MzN!MLA1BD-BD?5d_KzB-Kze!?1NASw1? r1K G]? r1xML?1nDMLrGjK°nDe!&w1?; kBDdxdfB nDe!? Njw1fG]d|MLe!? CxB_xBDd||e!wUjB_A1Gj?1CKSML?1A1wUCxdfxMLBpA1BDCHre!K=I+ gxBgCDTe ej? wUd|MLKzMLC|BpKLGw1C|Mze!? 0noOGjw GjNjB AUB_!ejKLw1&BjTXA1B`|MznDdfMze!?TsDKLBgn4dfxe!G]N!?1sDd|MLy8w1B]TB4dfn]; r ejw1 vnge!KzKLBD{CfGj?1CHnge!KzKL B o;vnDMT :]R .

(147). . . . . . .

(148). . . . . . . . . .

(149). . . 1. . 2. 3.

(150).

(151) RU;X>@?1A1BDCHKzML?1sgGj|MzC|sgBDClBg?sgKLGjCxd|MLnDMzdfs?1e!?+u®KLML?UsJGjMz|B 1.2. γ = 1.5 γ = 1.0 γ = 0.5. 1.1. X1. 1. X3. 0.9 0.8 0.7 0.6 0.5. X2. 0.4 0.3 0. 20. 40. 60. 80. 100. 120. 140. 160. 180. LM N!wU|BQRU;=<

(152) Bg&M=u®BgC|r1GjngBQO5Ir BD|sgKLGjCxd|MLy8w1BBg? N!fGj?UA nDMLCfG]MLKLKzBg&Bg?5d x = X T T T°e γ BDCxd~K Gy8wGj?5dfM=dfs A1BngMLC|GjMLKzKLBD-BD?8d -ej?¤r BDwUd x = X x = X + γX r BD?1C|BDrGj£B4³+BD-r1KzB}w1? G]1C|e!x BDw1AUBHCxBgngejw1C|CxBgC{C|MzC|&MLy8w1BDC¢Cxe!w1CwU? d|ML&Bg?5dJ; ` ngBQ} KmGjnDe!w1Cxd|e]uvsDK GjCdfMzngMzd|sjT{e!? rBgwUdA1s4dfBD|&ML?1BD C|e!? sDdfG]dA1BA1s4e!|-G]dfMze!?; 0ML?UC|MTK G+M=dfBDC|C|B@]GjxMLBHBg? e!?1n4dfMze!? A1BpK/bGj?UN!KLBA1Bpr1xe!rGjN5GdfMLej?BDdlA1BpK Gyw1Gj?5dfMzd|s A1B¢nDMLC|GjMLKzKLBg&Bg?5d )rGj(B4³+BD-r1KzBjT]KLBgC(-G³+ML-GlBDd-Mz?1ML-GlA1BKLGEM=dfBgCxC|B¢A1B¢K/mej?1A1B£A1B C|w10GjngBEe!?5d£KLMzBgwAGj?UC£KzBgC°A1Mz|BDnDdfMze!?1C°A1BEr1Kzw1C N!fG]?1A1BgC A1MzK G]dfG]dfMze!?2B4d£nge!&r1|BDC|CxMLe!?T |BgCxr BDnDd|Mz!BD-BD?5dJTXA1e!?5de!?r BDwUdA1e!?1npd||e!wUjBgEKSe!xMLBg?5dfG]dfMze!?; . . . 2. 2. 3. 3. 1. 1. 1.

(153). . 1. 1. 8. 1. v2. 7. µ1. 6. µ3 5. µ2 4. 3. 2. 1. φ 0. 0.2. 0.4. 0.6. 0.8. 1. 1.2. 1.4. 1.6. cisaillement. LM N!wU|B_RU; : 0Hxd g|B2C|e!w1&MLCxB}wU? N!fG]?1AngMzCfGjMzKLKLBD-BD?5d E]GjxM G]d|MLe!?A1BKLG&Mzd|BgCxC|B 0?1e!xG]KLMLCxsgB¢rGj°fG]r1r ejxd£}pngBDKLKLB{AZmw1?UBej?1A1BEA1Bl!ejKLw1&B ªASw1?1BEe!?UA1BGjnge!wUCxdfMzy8w1B A1B-Cxw1x0G]ngB&Bg?©ej?1nDd|MLe!?QA1B&K Gy8wGj?5dfM=dfs~A1B&ngMLC|GjMLKzKLBD-BD?8dg;->p?Q!ejMzdy8w1BKLGr1Gj|e!M Gjxd|sg|MzBgKzKLB{ASw1? O1e!&&BAUBpWjiG]?1CCxB xMLN!MzA1M 1B < gxB@GjCI-rUd|ejdfB!BDxdfMznJGjKzB °1MLBD? G7]Gj?5dy8w1B nDBgKzKLBAZmw1? O1ej-&BA1B :]VQGj?1C /: g&B GjCI-rUd|ejdfB 4;QvngM/T KmGjd gxB BgCd -eA1sgKzMLCxsgBr1GjlKLB-eA gKzBA1B pBg?5dgT1y8w1M|BD?1A df gC{1MzBg? ngej-rUd|B@A1wfG]MLA1MzC|C|BD-BD?5d A1BgC{!BDML?1BDCHCxe!w1CEKSB+ BDdASw1?1Bpd|Bg?1CxMLe!?; :]V . . . .

(154). . . .

(155). . .

(156) UR ;X>@?1A1BDCHKzML?1sgGj|MzC|sgBDClBg? sgKLGjCxd|MLngM=dfsH?1e!?+u®KLML?UsJGjMz|B ej?s4dfw1AUMLB@K/me!?UA1BpA1Bcd|e!?1BgKzBDI-!e7I5GjNjBJGj?5dKLB@Kze!?1NAUBKLG21MzC|C|BDnDd||MLnDBpA1BpKmGj?1NjKLBAUB AUsgnJG]K GjN!B]TªKze!|CxywUBKLBDC2A1Mz|BDnDdfMze!?1Cr1|Mz?1ngMzrGjKzBgCAmwU?¤C|e!KzMLA1B&?1B-C|e!?5drG]CGjKzMLN!?1sDBgC GJjBgnKLBgCEA1Mz|BDnDdfMze!?1ClrU|ML?UngMLr1GjKLB@AUBK/bG]wUdfxBpC|e!KzMLA1B]TU!e!Mz MLNjw1|B@VU; :+;.°mGj?GjK=IC|B`BgCd AUsD!BDKLe!rUr sDB BD?8d|M D|Bg&Bg?5dgT xw1C|y8wm}©K/ms4doGjUKLMLCxC|BD-BD?8d~AUBK/msDy8wG]dfMze!? A1BK G MzdfBDC|CxB Cxe!w1C)e!|&B B4³+r1KzMLngM=dfB]; °?_r1|BD?Gj?5d KLG{M=dfBgCxC|B¢sgN5GjKzB£}tDsg|eHAGj?1C(ngB4d|d|B¢A1BD|?1M gxBjTjej? ejUdfMzBg?5d(KLB£ng|M=d D|B A1BUMzw1xnJG]d|MLe!?T7y8w1MA1e!?U?1B¢KzB°doGjw+³_A1B£ngej-r1xBgCxC|MLej?_nD|Mzd|MLy8w1B£Gjw+u AUBgK }A1w1y8w1BDK KLG_Cxd||w1n4dfw1xBjT+BDd¢A1e!?1nHKLB xe!ML?5dJT8A1B4MLBg?U?1Bg?5d{Mz?1CxdfGj1KLBDCgT5!ejMLkOGjr1M=df|B VU; ( #

(157)

(158)

(159) #

(160)

(161)

(162)

(163)

(164) (!) !) ! ! *, UmGjM8sDd|w1A1Mzs¢A1BDCªe!?UA1BgCML? ?UMzdfsDC|MzGjKzBgCAUBlFG7IKzBgMLNjOejw2A1Blcdfe!?UBgKLB4I`C|B¢r1|e!r1GjN!BJG]?8d A1Gj?1C@A1BDCpA1Bg&M=u®BgCxrGjngBDCp|BD?1A1w1C`Gj?UMLC|e]df|ejr BDCrGjA1BN!|Gj?1A1BDCpA1sDe!xGdfMLej?1CHCdoGu d|MLy8w1BDC O1ej-e!N g?1BDCKze!|Cxy8w1BQKLBgC-G]dfsD|MLGjw+³Cxe!?5dCxw xBDd|C} w1?1B '

(165) $ ) MzC|ejd||e!rBGj|UMzdf|GjMLxBj; .°mMz?8d|sg ,Dd¢A1BnDBgCs4dfw1AUBgCBDCxdl}KLGè!MzC B4³+r sD|Mz-BD?8dfGjK ªKzM GjMzC|e!? AUB BgKzKlr ejw1A1BDC&&sDdfGjw+³¤|BgnDw1Mzd|CdfBDKLCy8w1BGjKLwU-Mz?1MLw1T(ngw1M=+xBjT£tgMz?1n KzM GjMzC|e!? AZ °|Mzn 8C|Bg? r e!wUAUBgCng|MzCxdfGjw+³Q-GjngKzsgC KLM G]MLC|ej? AmGjMLxB&re!w1pKzBgC`&Bg1|Gj?1BDCAUB NjKLe!1wUKLBgC{xe!w1N!BDCgTB4dfnj; XBDddfO1sDe!|Mzy8w1B £KLGKLM G]MLC|ej? ASML?1nDe!-rU|BgCxC|Mz1MLKzMzdfsHBgCdBD? BZB4d B ³+ngBgr+dfMLej?1?1BgKzKLBnJGj£K G`rGjdfMzBAUwdfBD?1C|BDw1A1BDCnDe!?5dffG]ML?5dfBDCy8w1MKLw1MBDCxd{G]C|C|engMzsgBBgCd Cxr1O1sD|MLy8w1B]TXngB`y8w1M?SBgCxdHrGjCE?1sDngBDC|CfG]ML|BD-BD?5dKzB@nJGjCre!w1{w1?1B`KzM GjMzC|e!? Njsg?1sD|MLy8w1B]; ( #

(166)

(167)

(168) !'+(!) & , .e!xC|y8wSe!? sDd|w1A1MLBKLBgCej?1A1BgCAUB!e!Kzw1&BjT°e!? CgSML?5d|sg|BDC|CxBBD? N!sg?1sDfGjKGjw+³¤e!?1A1BDC OUe!-ejN g?1BDCgT8re!w1°KLBDC|y8w1BDKLKLBDC KmGj-rUKLMzd|w1A1B¢|BgCdfBEngej?1CxdfGj?5dfB MzN!w1|BER+;bR ªe!w&]GjxMLB A1Gj?1CK GA1MLxBgnDd|MLe!?QA1B-r1|ejrGjN5G]d|MLe!? MLN!wU|B~RU;mR ; G]d|O1sg-G]dfMzy8w1Bg&Bg?5dJT(e!?©KLBgC xBgr1xsgCxBg?5dfB_rGj{A1BDCHA1sDr1K G]ngBg&Bg?5d|CAUBKLG2e!|&B B n];mn]; , 0RU;bR+;z< u=a + e BgCxd KzB!BDnDd|Bgw1 /}@nDe!-re!C|Gj?5dfBgC°xsgBDKLKLBDCAUB{r e!KLGj|MzCfG]d|MLe!?ZT ω BDCxd£K GrUw1KLC|G]dfMze!?T a BgCd_KzB2!BDnDd|Bgw1w1?1M=doGjMz|B 0} nge!&r ejCfGj?5dfBDC`|sgBDKLKzBgCAGj?1C`K G AUML|BDnDd|MLe!?A1BrU|e!r+u n G]N5G]dfMze!?TB4d s BgCd2KLG KLBD?8d|Bgw1`CxnJGjKLGjMLxBj; @wGj?UA s BDd ω C|e!?5d|sDBgKLKzBgCDT(K/bG]-r1KzMzd|w1A1B ?UB]GjxMLB`rGjC y8wGj?UA BDCxdnge!&r1KLB ³+BjTXKmGj&r1KLM=dfw1A1BBgCxdG]dxdfsg?8w1sDBGJ!BDn2KzBd|Bg&r1

(169) C y8wG]?1A s BgCxdnDe!-rUKLB4³+ωB]T1KmGj&r1KLM=dfw1A1BHBgCdG]-e!dfMzB 0e!wGj&r1KzM sDB GJ!BDn_K/mBDC|rG]ngBj; ke!&&Be!? K/bG+wZT1KLBDCe!?1AUBgC )

(170)

(171) xe!w1BD?8dlw1? KzBr1xsgre!?1A1sDfGj?5d{BD? sDK GjCdfMzngMzd|sj;(²ejw1ªnDBgC e!?UA1BgCDT!KmGj&r1KLM=dfw1A1BjG]|MLB£C|Mz?8w1C|e!MzAGjKzBg&Bg?5d(AGj?1CK GEA1MLxBgnDd|MLe!? AUBr1|e!r1GjN5G]d|MLe!? BDd BDCxdG]dxdfsg?8w1sDBQAGj?1C wU?1BQGjwUd||B A1Mz|BDnDdfMze!?T{!ejML MLN!w1xB RU;SV1; |ejwU!BD`d|e!wUd|BgCpKLBDCpC|e!KzwUdfMze!?1C@AUBgCpsgy8wGdfMLej?1CpA1wQ-ejwU!BD-BD?8d`Cxe!w1Cpe!x-BAZmw1?UB :jq . . . . . . . . . . .

(172).

(173). . . . . . . . . 1. . 2. ω(sn·x−t). . .

(174). . . .

(175) RU;X>@?1A1BDCHKzML?1sgGj|MzC|sgBDClBg?sgKLGjCxd|MLnDMzdfs?1e!?+u®KLML?UsJGjMz|B. LM N!wU|BpRU;mR £>@?1A1BDCHAUB`je!KLwU-BpO1ej-e!N g?1BDC e!?1A1BQML?UO1e!&e!N g?UB BgCdw1?UBQdfGjnoO1BGjxA1w1BjTA1w 0G]MzdA1BDC?Ue!1xBgw1CxBgCA1MLxBgnDd|MLe!?UC BDd`ML?Unge!?1?8w1BDCg; ?1B~r1|engsDA1w1|B~CI+CdfsDG]d|MLy8w1B~A1B~|sDC|e!KzwUdfMze!?QG sDd|s~sgK G] e!xsgBrG] e!w1KLGj?1N!BDBDd GJI!BDC <7YjY!R4TBD?2rGjdoGj?5dA1B£K GE|BgrU|sgCxBg?5doGdfMLej?2C|wUMz]Gj?5dfB£A1BgCe!?1A1BDC ML?1O1ej-e!N g?1BDCgT B nj;Snj; /RU;mRU;b: + u=A vngMTKzB jBgn4dfBgwUªA1B re!K GjxMLC|G]dfMze!? A rBgwUd ,Dd||B ngej-r1KzB4³+BjTA1B£ ,D-B°y8w1B£K G{r1wUKLCfGdfMLej? BDd°KzB£jBgn4dfBgwU°A1BgC KzBg?5dfBDw1|C ; .BDCª!BDnDdfBDw1|C nDe!-rUKLB4³+BDCªC|ej?8d°Gjr1rBgKLsDC " ω BDd_KLBgwU2GjKzN gU|B&BgCxd2rGje!MLC`SA1sD|e!wUdfGj?5dfB GjML?UC|M A1Bgw³ UMz!BDnDd|Bgw1xC A BDd B rBgwu !Bg?5d ,Dd||B }KLGejMLC r1GjfGjKzK DKLBgC * A × B = 0BDd&e!dfO1ejN!e!?Gjw³ A · B = 0 nge!&-B A = (1, M , 0) B4d B = (2M , −2, 0) ywUM¢r1Kzw1C2BDCxdgT°ngBgC2A1Bgw+³©!BDnDd|Bgw1xCBg? rGjxd|MLnDw1KLMzBg`C|e!?5d vMLCxejdfxe!r BDC A · A = B · B = 0 ; ?1BejMLC2nDBDdxdfB GjKzN gU|B GjC|CxML&MLKLsDBjTKSe!Ud|Bg?5dfMze!? BDdEKLGngK G]C|C|M nJGdfMLej? CxICxd|sg-G]dfMzy8w1BÀ1B@dfe!w+dfBgCEKzBgC{C|ejKLwUd|MLe!?1C C|BÀ1sgxe!w1KzBg?5dA1Bp0G#ge!??Gdfw1xBgKLKzBj; 0HML?1CxM DbGjMprUw e!Ud|Bg?1Mzd|e!wUd|BgCKLBgCC|ejKLwUd|MLe!?1CA1BK G e!x-B /R+;bRU;b: re!w1w1? G]d|sgxM GjwA1B ee!?1B4I5u FEMzKLMz? ML?1nDe!-rU|BgCxC|Mz1KLB )A1s4e!|&s@Pmq\UBDd re!w1ªw1?-G]dfsD|M G]w A1B GjA1GjG]|A 0nDe!&r1|BDC|C|Mz1KLB _A1s4e!|&sPS[]\;

(176) B r1Kzw1C DbG]MlsDdfGj1KLM¢y8w1BgKdvIrBA1B G]d|sgxM GjwT w1?1Be!MzC@A1sDej|&sjTrBg|&BDd@K G r1xe!rGjN5GdfMLej? ASe!?1A1BDC_r1KLGj?1BDC KLej?1N!Mzd|w+u A1ML?G]KLBgC A × S = 0A1Gj?1C{dfe!w+dfBgCEKzBgCEA1MLxBgn4dfMLej?1C`P=<JY]\; .BDC@Gjr1rUKLMLngG]dfMze!?1CEA1B_K G&d|O1sgej|MLBA1BDC@e!?1A1BDCMz?1O1e!&e!N D?1BgCC|e!?5dpMz?1?1e!21fGjUKLBgC nge!&-Be!? r BDwUd&KLB ngej?1CxdfG]dfBD&MzngMlB4d&rGjB4³+BD-r1KzB}K GKLBDnDdfwU|B A1BKmGjdfMLnDKLB-A1B |BDw1B`rG]

(177) BgngKzBgxnB4dHGjK; /:ji!i5q4; . . . . . . . ω(S·x−t). . . . . . . .

(178). . . . . . :j[.