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41614 D Jhqhudo Vroxwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8

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418 H{dpsohv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 46

41814 Fodpshg0Fodpshg Odplqdwh 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 47

41815 Fdqwlohyhu Odplqdwh 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4:

41816 Fodpshg0Vlpso| Vxssruwhg Odplqdwh 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4;

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515 Irupxodwlrq ri wkh sureohp 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 74

516 D vroxwlrq ri wkh jryhuqlqj gl>huhqwldo htxdwlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 76

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51: Uhvxowv dqg Glvfxvvlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7;

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51:15 Fodpshg sodwhv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 88

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614 Lqwurgxfwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :8

615 Irupxodwlrq ri wkh sureohp 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :9

616 Vroxwlrq ri wkh sureohp 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;3

61614 D jhqhudo vroxwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;3

61615 D vhulhv vroxwlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;5

617 Vdwlvidfwlrq ri erxqgdu| dqg lqwhuidfh frqglwlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;8

618 Uhvxowv dqg Glvfxvvlrq 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;9

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619 Frqfoxvlrqv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <:

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416 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv iru d fodpshg0fodpshgkrprjhqhrxv sodwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 58

417 D{ldo glvsodfhphqw glvwulexwlrq rq wkh vhfwlrq %� ' u*e iru d fodpshg0fodpshg krprjhqhrxv sodwh iru irxu ydoxhv ri u*M1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 59

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419 Qrupdo vwuhvv glvwulexwlrq dw %� ' u*2 iru d fodpshg0fodpshg krprjhqhrxvsodwh iru irxu ydoxhv ri u*M1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5;

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41< Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv iru d fdqwlohyhu krprjh0qhrxv sodwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 64

4143 Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv iru d fdqwlohyhu krpr0jhqhrxv sodwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 65

4144 Yduldwlrq rq irxu sodqhv ri wudqvyhuvh qrupdo vwuhvv iru d fodpshg0vlpso|vxssruwhg wkuhh0od|huhg odplqdwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 66

4145 Yduldwlrq ri orqjlwxglqdo vwuhvv rq irxu sodqhv iru d fodpshg0vlpso| vxssruwhgwkuhh0od|huhg odplqdwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 67

4146 Glvwulexwlrq ri wkh orqjlwxglqdo vwuhvv rq irxu vhfwlrqv iru d fodpshg0vlpso|vxssruwhg wkuhh0od|huhg odplqdwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 68

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4147 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv iru d fodpshg0vlpso|vxssruwhg wkuhh0od|huhg odplqdwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 69

4148 Glvwulexwlrq ri vkhdu vwuhvv jô2 rq irxu vhfwlrqv iru d fodpshg0vlpso| vxs0sruwhg wkuhh0od|huhg odplqdwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6:

4149 Glvwulexwlrq ri wkh d{ldo glvsodfhphqw rq irxu vhfwlrqv iru d fodpshg0vlpso|vxssruwhg wkuhh0od|huhg odplqdwh1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6;

514 D Q0od|hu odplqdwhg uhfwdqjxodu sodwh 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 75

515 Qrupdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d vtxduh sodwh dw %2 'O2*2 +Fdvh+4,/ Frq?jxudwlrq E�E�/ Ordg +d,/ O�2K @ 8/ g�@583 whupv,1 1 1 1 1 1 1 1 1 99

516 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq iru irxu gl>huhqw erxqgdu| frqglwlrqv+Fdvh +4,/ Ordg +d,/ O2@O�/ O�2K@8/ g�@583 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 9:

517 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq iru irxu gl>huhqw erxqgdu| frqglwlrqv+Fdvh +4,/ Ordg +d,/ O2@O�/ O�2K@8/ g�@583 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 9;

518 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq iru irxu gl>huhqw erxqgdu| frqglwlrqv+Fdvh +5,/ Ordg +d,/ O2@O�/ O�2K@8/ g�@533 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 9<

519 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq iru irxu gl>huhqw erxqgdu| frqglwlrqv+Fdvh +5,/ Ordg +d,/ O2@O�/ O�2K@8/ g�@533 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 :3

51: Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq iru irxu gl>huhqw erxqgdu| frqglwlrqv+Fdvh +5,/ Ordg +d,/ O2@O�/ O�2K@8/ g�@533 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 :4

51; Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d sodwh wkdw lv vlpso|vxssruwhg rq wzr hgjhv dqg wudfwlrq0iuhh rq wkh rwkhu wzr +Fdvh +5,/ Ordg+d,/ O2@O�c O�2K @ 8/ g�@533 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :5

51< Wkh fkdqjh lq wklfnqhvv ri d sodwh wkdw lv vlpso| vxssruwhg rq wzr hgjhv dqgwudfwlrq iuhh rq wkh rwkhu wzr 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 :6

614 Wkh slh}rwkhuprhodvwlf odplqdwhg sodwh 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ::

615 Fdqwlohyhu sodwh zlwk d vxuidfh prxqwhg S]W dfwxdwru sdwfk 1 1 1 1 1 1 1 1 1 <8

616 Orqjlwxglqdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv iru d fodpshg0fodpshg odplqdwh437

617 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d 77 odplqdwh 1 1 1 1 438

618 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3` ä7 odplqdwh+u*M @8, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 439

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61< Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d 77 odplqdwh1 1 1 1 1 443

6143 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d 77 odplqdwh1 1 1 1 1 444

6144 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ä8 odplqdwh1 1 1 1 445



6147 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu sodqhv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +d, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 448

6148 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu sodqhv ri d ^32<3232S]W` ä8odplqdwh forvh wr wkh iuhh hgjh1 Ordg Fdvh +d, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 449

6149 Hohfwulf srwhqwldo lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +e, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44:

614: Hohfwulf srwhqwldo lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +f, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44;

614; Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +e, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44<

614< Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +f, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 453

6153 Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +e, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 454

6154 Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +f, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 455

6155 Glvwulexwlrq ri wkh phfkdqlfdo d{ldo glvsodfhphqw rq irxu vhfwlrqv ri d ^32<3232S]W`ä8 odplqdwh1 Ordg Fdvh +d, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 456

6156 Glvwulexwlrq ri wkh phfkdqlfdo d{ldo glvsodfhphqw rq irxu vhfwlrqv ri d ^32<3232S]W`ä8 odplqdwh1 Ordg Fdvh +e, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 457

6157 Orqjlwxglqdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` ää odpl0qdwh1 Ordg Fdvh +f, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 458

{

6158 Orqjlwxglqdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` ää odpl0qdwh1 Ordg Fdvh +d, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 459

6159 Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` 77odplqdwh1 Ordg Fdvh +d, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 45:

615: Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` 77odplqdwh1 Ordg Fdvh +e, +u*M @8,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 45;

615; Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq wkuhh sodqhv vhfwlrqv ri d fdqwlohyhuodplqdwh zlwk d S]W sdwfk 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 45<

615< Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq rq wkuhh sodqhv vhfwlrqv ri d fdqwlohyhuodplqdwh zlwk d S]W sdwfk 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 463

6163 Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d fdqwlohyhu odplqdwhzlwk d S]W sdwfk 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 464

6164 Wudqvyhuvh glvsodfhphqw rq wkuhh sodqhv ri d fdqwlohyhu odplqdwh zlwk d S]Wsdwfk 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 465

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Olvw ri Wdeohv

414 Wudqvyhuvh gh hfwlrq/ orqjlwxglqdo vwuhvv/ wudqvyhuvh vkhdu vwuhvv/ wudqvyhuvhqrupdo vwuhvv dqg h{whqvlrq ri wkh qrupdo iru lqfuhdvlqj vsdq0wr0wklfnqhvvudwlrv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4:

514 Qrphqfodwxuh iru erxqgdu| frqglwlrqv suhvfulehg dw %� ' f ru O�é 1 1 1 1 1 1 93

515 Frqyhujhqfh vwxg| iru d vtxduh odplqdwh wkdw lv vlpso| vxssruwhg rq wzrrssrvlwh hgjhv dqg fodpshg rq wkh rwkhu wzr +Fdvh +4,/ Ordg +d,/ O�*K' D,1 93

516 Glvsodfhphqwv dqg vwuhvvhv iru d vtxduh odplqdwh vxemhfwhg wr hljkw gl>huhqwerxqgdu| frqglwlrqv +Fdvh +4,/ O�2K@8/ N�@583 whupv,1 1 1 1 1 1 1 1 1 1 1 1 94

517 Glvsodfhphqwv dqg vwuhvvhv iru d vtxduh odplqdwh vxemhfwhg wr hljkw gl>huhqwerxqgdu| frqglwlrqv +Fdvh +4,/ O�2K@43/ N�@583 whupv,1 1 1 1 1 1 1 1 1 1 1 95

518 Glvsodfhphqwv dqg vwuhvvhv iru d vtxduh odplqdwh vxemhfwhg wr hljkw gl>huhqwerxqgdu| frqglwlrqv +Fdvh +5,/ N�@533 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 96

519 Wkurxjk0wklfnqhvv glvsodfhphqw dqg vwuhvv glvwulexwlrqv iru d vtxduh odplqdwh+Fdvh +5,/ Frq?jxudwlrq E�E�c Ordg +d,/ O�2K@8/ N�@533 whupv,1 1 1 1 1 1 97

51: Frqyhujhqfh vwxg| iru d krprjhqhrxv fr sodwh fodpshg rq doo hgjhv +Ordg+d,/ O�*K@43/ O2*O�@318,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 98

51; Glvsodfhphqw dqg vwuhvvhv iru d uhfwdqjxodu odplqdwh fodpshg rq doo hgjhv+Ordg +d,/ O�*K@8/ O2*O�@318/ N�@58 whupv,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 98

614 Qrq0ydqlvklqj pdwhuldo surshuwlhv ri wkh judsklwh0hsr{| dqg S]W08D od|huv1 ;:

615 Glvsodfhphqwv dqg vwuhvvhv iru d ^32<3` odplqdwh vxemhfwhg wr irxu gl>huhqwerxqgdu| frqglwlrqv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;<

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Wkh Jhqhudol}hg Sodqh VwudlqGhirupdwlrqv ri DqlvrwurslfFrpsrvlwh Odplqdwhg Sodwhv

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Zh xvh wkh Hvkhoe|0Vwurk irupdolvp wr dqdo|}h wkh jhqhudol}hg sodqh vwudlq txdvlvwdwlf gh0irupdwlrqv ri dq dqlvrwurslf/ olqhdu hodvwlf odplqdwhg sodwh1 Wkh odplqdwh frqvlvwv ri krpr0jhqhrxv odplqdh ri duelwudu| wklfnqhvvhv1 Frpsxwhg uhvxowv duh suhvhqwhg iru wkuhh vdpsohsureohpv wr looxvwudwh wkh h>hfw ri erxqgdu| frqglwlrqv dqg ri wkh vsdq wr khljkw udwlr1

3D voljkwo| prgl?hg yhuvlrq ri wklv fkdswhu kdv ehhq vxeplwwhg iru sxeolfdwlrq lq wkh Lqwhuqdwlrqdo Mrxuqdori Vrolgv dqg Vwuxfxwuhv1

4

5

414 Lqwurgxfwlrq

Sdjdqr +4<9<, xvhg wkh olqhdu hodvwlflw| wkhru| wr dqdo|}h txdvlvwdwlf ghirupdwlrqv ri dq

ruwkrwurslf vlpso| vxssruwhg odplqdwhg sodwh xqghu wkh dvvxpswlrq ri sodqh vwudlq ghiru0

pdwlrqv dqg frpsduhg klv uhvxowv zlwk wkrvh rewdlqhg e| xvlqj wkh fodvvlfdo sodwh wkhru|1

Phohvknr +4<<:, kdv uhfhqwo| uhylhzhg wkh klvwru| dqg vwudwhjlhv iru ?qglqj dqdo|wlfdoo| glv0

sodfhphqwv dqg vwuhvvhv lq d fodpshg0fodpshg wklq sodwh ri duelwudu| ohqjwk wr zlgwk udwlr1

Dv lv fohdu iurp Phohvknr*v sdshu/ wkhuh kdv ehhq vljql?fdqw lqwhuhvw lq ?qglqj dq dqdo|wlfdo

vroxwlrq ri wkh qrqkrprjhqhrxv elkduprqlf htxdwlrq iru erxqgdu| frqglwlrqv vlpxodwlqj

fodpshg hgjhv> d elkduprqlf htxdwlrq prghov ehqglqj ghirupdwlrqv ri d wklq sodwh1 Zh

uhihu wkh uhdghu wr Phohvknr +4<<:,/ Ndsdqld dqg Udflwl +4<;<,/ Qrru dqg Exuwrq +4<;<,/

Vrogdwrv dqg Zdwvrq +4<<:,/ Mrqhv +4<:8, dqg Uhgg| +4<<:, iru d klvwrulfdo shuvshfwlyh dqg

iru d uhylhz ri ydulrxv dssur{lpdwh sodwh wkhrulhv1 Dv idu dv zh fdq dvfhuwdlq/ wkh fkdoohqjlqj

sureohp ri ?qglqj dq dqdo|wlfdo vroxwlrq ri wkh olqhdu hodvwlflw| htxdwlrqv jryhuqlqj ghiru0

pdwlrqv ri d fodpshg0fodpshg sodwh ri duelwudu| vsdq wr wklfnqhvv udwlr uhpdlqv xqvroyhg1

Khuh zh suhvhqw dq dqdo|wlfdo vroxwlrq ri wkh f|olqgulfdo ehqglqj ri d fodpshg0fodpshg/

dqlvrwurslf/ olqhdu hodvwlf sodwh ri duelwudu| vsdq wr wklfnqhvv udwlr1 Dv looxvwudwhg e| uhvxowv

iru fodpshg0iuhh/ dqg fodpshg0vlpso| vxssruwhg odplqdwhv/ rxu irupxodwlrq dgplwv gl>huhqw

erxqgdu| frqglwlrqv1 Wkuhh0glphqvlrqdo htxdwlrqv ri olqhdu hodvwlflw| vlpsol?hg wr wkh fdvh

ri jhqhudol}hg sodqh0vwudlq ghirupdwlrqv duh vroyhg e| wkh Hvkhoe|0Vwurk irupdolvp1 Wkxv

wkh jryhuqlqj htxdwlrqv duh h{dfwo| vdwlv?hg/ dqg ydulrxv frqvwdqwv lq wkh jhqhudo vroxwlrq

duh ghwhuplqhg iurp wkh erxqgdu| dqg wkh frqwlqxlw| frqglwlrqv dw wkh lqwhuidfhv1 Wklv

uhvxowv lq dq lq?qlwh v|vwhp ri htxdwlrqv lq lq?qlwho| pdq| xqnqrzqv1 Wkh wuxqfdwlrq ri

wklv vhw ri htxdwlrqv lqhylwdeo| lqyroyhv vrph huuruv zklfk fdq eh plqlpl}hg e| lqfuhdvlqj

wkh qxpehu ri whupv lq wkh vhulhv1 Wkh surfhgxuh lv looxvwudwhg e| frpsxwlqj uhvxowv iru wkh

f|olqgulfdo ehqglqj ri d sodwh ri duelwudu| vsdq wr wklfnqhvv udwlr dqg hlwkhu uljlgo| fodpshg

6

dw erwk hgjhv ru fodpshg dw rqh hqg dqg vlpso| vxssruwhg dw wkh rwkhu1 Wkhvh uhvxowv

vkrxog khos rwkhuv frpsduh wkh suhglfwlrqv ri dssur{lpdwh sodwh wkhrulhv zlwk wkh dqdo|wlfdo

vroxwlrq dqg wkxv dvvhvv wkh dffxudf| ri wkhlu sursrvhg sodwh wkhrulhv1

415 Irupxodwlrq ri wkh Sureohp

Zh xvh d uhfwdqjxodu Fduwhvldq frruglqdwh v|vwhp/ vkrzq lq Ilj1 414/ wr ghvfuleh wkh lq?q0

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uhjlrq dfc uo û Eý4c4ä û dME�äcMEùn�äo lq wkh xqvwuhvvhg uhihuhqfh frq?jxudwlrq1 Sodqhv

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odplqdh/ dqg wkh wrs erxqglqj vxuidfh1 Htxdwlrqv jryhuqlqj wkh glvsodfhphqwv ý ' ýj

ri d pdwhuldo srlqw j duh

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jðæ ' äðæ&,ü&c, c +415,

äðæ&, ' äæð&, ' ä&,ðæ é +416,

Khuh lv wkh suhvhqw srvlwlrq ri wkh pdwhuldo sduwlfoh wkdw rffxslhg sodfh j lq wkh uhihuhqfh

frq?jxudwlrq/ jðæ lv wkh Fdxfk| vwuhvv whqvru/ äðæ&, duh hodvwlf frqvwdqwv/ d frppd iroorzhg

e| lqgh{ æ lqglfdwhv sduwldo gl>huhqwldwlrq zlwk uhvshfw wr %æ/ dqg d uhshdwhg lqgh{ lpsolhv

vxppdwlrq ryhu wkh udqjh ri wkh lqgh{1 Zh zloo lqwhufkdqjhdeo| xvh wkh gluhfw dqg lqglfldo

qrwdwlrq1 Pdwhuldo hodvwlflwlhv duh dvvxphg wr |lhog d srvlwlyh vwudlq hqhuj| ghqvlw| iru hyhu|

qrq0uljlg ghirupdwlrq ri wkh erg|1

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h{whqw lq wkh %2 gluhfwlrq/ dqg hodvwlflwlhv duh frqvwdqwv1

416 Vroxwlrq ri wkh Sureohp

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wr eh ghwhuplqhg1 Vxevwlwxwlrq ri +41;, lqwr +415, dqg wkh uhvxow lqwr +414, jlyhv

i"n RE+n+A ä n R2Aj@ ' fc +41<,

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57

−30 −20 −10 0 10 20 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ11

/q0

x 3/H

x1/L =0

x1/L =0.05

x1/L =0.1

x1/L =0.5

Iljxuh 415= Orqjlwxglqdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv iru d fodpshg0fodpshg krpr0jhqhrxv sodwh +u*M ' e,1

58

−1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ31

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x 3/H

x1/L =0

x1/L =0.05

x1/L =0.2

x1/L =0.4

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59

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

100ETH2u

1/q

0L3

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−1.2

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5;

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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L/H =4 L/H =10L/H =20L/H =60

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5<

−0.3 −0.25 −0.2 −0.15 −0.1 −0.05 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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63

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0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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64

−2 −1.5 −1 −0.5 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

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0.9

1

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65

−0.5 −0.25 0 0.25 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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1

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66

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67

0 0.25 0.5 0.75 1

−40

−30

−20

−10

0

10

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30

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68

−20 −15 −10 −5 0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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69

−3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 30

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0.2

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6:

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0.7

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1

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1

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�DSdjdqr/ Q1 M1 dqg Kdw?hog/ V1 M1/ 3Hodvwlf ehkdylru ri pxowlod|huhg elgluhfwlrqdo frpsrv0

lwhv/4 DLDD Mrxuqdo/ Yro1 43/ 4<:5/ ss1<648<661

�SVulqlydv/ V1/ Mrjd Udr/ F1 Y1 dqg Udr/ D1 N1/ 3Dq h{dfw dqdo|vlv iru yleudwlrq ri vlpso|0

vxssruwhg krprjhqhrxv dqg odplqdwhg wklfn uhfwdqjxodu sodwhv/4 Mrxuqdo ri Vrxqg dqg

Yleudwlrq/ Yro1 45/ Qr1 5/ 4<:3/ ss14;:84<<1

�.Vulqlydv/ V1 dqg Udr/ D1 N1/ 3Ehqglqj/ yleudwlrq dqg exfnolqj ri vlpso| vxssruwhg wklfn ru0

wkrwurslf uhfwdqjxodu sodwhv dqg odplqdwhv/4 Lqwhuqdwlrqdo Mrxuqdo ri Vrolgv dqg Vwuxfwxuhv/

Yro1 9/ 4<:3/ ss14796847;41

�HUrkzhu/ N1/ 3Dssolfdwlrq ri kljkhu rughu wkhrulhv wr wkh ehqglqj dqdo|vlv ri od|huhg frp0

srvlwh sodwhv/4 Lqwhuqdwlrqdo Mrxuqdo ri Vrolgv dqg Vwuxfwxuhv/ Yro1 5</ Qr1 4/ 4<<5/ ss14388

44<1

�bOhh/ N1 K1 dqg Fdr/ O1/ 3D suhglfwru0fruuhfwru }lj0}dj prgho iru wkh ehqglqj ri odplqdwhg

frpsrvlwh sodwhv/4 Lqwhuqdwlrqdo Mrxuqdo ri Vrolgv dqg Vwuxfwxuhv/ Yro1 66/ Qr1 9/ 4<<9/

ss1;:<8;<:1

8<

2fPdx/ V1 W1/ Wrqj/ S1 dqg Sldq/ W1 K1 K1/ 3Ilqlwh hohphqw vroxwlrqv iru odplqdwhg sodwhv/4

Mrxuqdo ri Frpsrvlwh Pdwhuldov/ Yro1 9/ 4<:5/ ss163786441

2�Vslonhu/ U1 O1/ 3K|eulg0vwuhvv hljkw0qrgh hohphqwv iru wklq dqg wklfn pxowlod|hu odplqdwhg

sodwhv/4 Lqwhuqdwlrqdo Mrxuqdo iru Qxphulfdo Phwkrgv lq Hqjlqhhulqj/ Yro1 4;/ 4<;5/ ss1;348

;5;1

22Olrx/ Z1 M1 dqg Vxq/ F1 W1/ 3D wkuhh0glphqvlrqdo k|eulg vwuhvv lvrsdudphwulf hohphqw iru

wkh dqdo|vlv ri odplqdwhg frpsrvlwh sodwhv/4 Frpsxwhuv dqg Vwuxfwxuhv/ Yro1 58/ Qr1 5/ 4<;:/

ss1574857<1

2ôWlqj/ W1 F1 W1/ Dqlvrwurslf Hodvwlflw|1 Wkhru| dqg Dssolfdwlrqv/ R{irug Hqjlqhhulqj Vfl0

hqfh Vhulhv/ Qr 781 R{irug Xqly Suhvv/ Qhz \run/ 4<<91

2eHvkhoe|/ M1 G1/ Uhdg/ Z1 W1 dqg Vkrfnoh|/ Z1/ 3Dqlvrwurslf hodvwlflw| zlwk dssolfdwlrqv wr

glvorfdwlrq wkhru|/4 Dfwd Phwdooxujlfd/ Yro1 4/ 4<86/ ss1584858<1

2DVwurk/ D1 Q1/ 3Glvorfdwlrqv dqg fudfnv lq dqlvrwurslf hodvwlflw|/4 Sklorvrsklfdo Pdjd}lqh/

Yro1 6/ 4<8;/ ss195889791

2SWlqj/ W1 F1 W1/ 3H>hfwv ri fkdqjh ri uhihuhqfh frruglqdwhv rq wkh vwuhvv dqdo|vhv ri

dqlvrwurslf hodvwlf pdwhuldov/4 Lqwhuqdwlrqdo Mrxuqdo ri Vrolgv dqg Vwuxfwxuhv/ Yro1 4;/ Qr1 5/

4<;5/ ss146<84851

2.Ghpsvh|/ M1 S1 dqg Vlqfodlu/ J1 E1/ 3Rq wkh vwuhvv vlqjxodulwlhv lq wkh sodqh hodvwlflw| ri

wkh frpsrvlwh zhgjh/4 Mrxuqdo ri Hodvwlflw|/ Yro1 </ Qr1 7/ 4<:</ 6:686<41

2HNkghlu/ D1 D1 dqg Uhgg|/ M1 Q1/ 3Dqdo|wlfdo vroxwlrqv ri uh?qhg sodwh wkhrulhv ri furvv0so|

frpsrvlwh odplqdwhv/4 Mrxuqdo ri Suhvvxuh Yhvvho Whfkqrorj|/ Yro1 446/ 4<<4/ ss18:388:;1

93

Wdeoh 514= Qrphqfodwxuh iru erxqgdu| frqglwlrqv suhvfulehg dw %� ' f ru O�é

Qrwdwlrq EF dw {� @ 3 ru O� Fruuhvsrqglqj LE�äü ru ME�äü QdphE� x� @ x2 @ xô @ 3 gldj^4> 4> 4` Fodpshg vxuidfhE2 x� @ x2 @ â�ô @ 3 gldj^4> 4> 3` 0Eô x� @ â�2 @ xô @ 3 gldj^4> 3> 4` 0Ee x� @ â�2 @ â�ô @ 3 gldj^4> 3> 3` Volsshu| vxuidfhED â�� @ x2 @ xô @ 3 gldj^3> 4> 4` Vlpso| vxssruwhgES â�� @ x2 @ â�ô @ 3 gldj^3> 4> 3` 0E. â�� @ â�2 @ xô @ 3 gldj^3> 3> 4` 0EH â�� @ â�2 @ â�ô @ 3 gldj^3> 3> 3` Wudfwlrq0iuhh vxuidfh

Wdeoh 515= Frqyhujhqfh vwxg| iru d vtxduh odplqdwh wkdw lv vlpso| vxssruwhg rq wzr rssrvlwhhgjhv dqg fodpshg rq wkh rwkhu wzr +Fdvh +4,/ Ordg +d,/ O�*K' D,1

N� çxô++K@5,ã, çâ��+3, çâ22+K, çâôô++K@5,ã, çâ�2+3, çâ2ô++K@5,ã, çâô�++K@5,ã, çh

584=554 5794=554 4<9

ý7=96; 6;8 8=:76 4343=8:7 4753=8;4 ;4:

3=647 48:3=;:9 9453=;:: 69:

4=869 8444=86; 7;4

8=5;3 573

834=54; ;<84=54; <33

ý7=958 575 8=:5< 6463=8:< :683=8:: 445

3=646 :4<3=;:8 :963=;:8 864

4=887 ;::4=887 7:6

8=598 5<5

4334=54: ;:94=54: ;:8

ý7=965 834 8=:58 8963=8:; 8833=8:< 493

3=646 6563=;:8 3<83=;:8 48;

4=88: 69<4=88: 7<<

8=59; 968

4834=54: 8<74=54: 8<7

ý7=95< 597 8=:56 98<3=8:; <633=8:; 7;3

3=646 5863=;:7 <<73=;:7 <97

4=885 :934=885 ;36

8=59: 4;3

5334=54: 84;4=54: 84;

ý7=964 834 8=:56 :593=8:; :533=8:; <73

3=646 5733=;:7 <663=;:7 <83

4=884 5834=884 585

8=59: ;4:

5834=54: 7:44=54: 7:4

ý7=95< <;3 8=:56 4;73=8:; ;7;3=8:; 977

3=646 5673=;:7 <553=;:7 <43

4=883 6554=883 5<8

8=59: 6:7

94

Wdeoh 516= Glvsodfhphqwv dqg vwuhvvhv iru d vtxduh odplqdwh vxemhfwhg wr hljkw gl>huhqwerxqgdu| frqglwlrqv +Fdvh +4,/ O�2K@8/ N�@583 whupv,1

Wkhru| Yduldeoh E�E� E2E2 EôEô EeEe EDED ESES E.E. EHEHDqdo|wlfdo/ Ordg +d, çx�+K, 04137: 031845 041383 031676 041;:3 031;7: 041<57 031898

çx2+3, 41674 51965 41693 6157: 41;<< 51:4: 41<94 615<4çxô+K@5, 4154: 51579 4155< 51:3; 41:45 5165: 41:8; 51:86çâ��+3, 071963 0517<< 07199: 041<<7 0:19:4 06178: 0:1<46 051993çâ22+K, 81:56 43189; 81::4 451:38 :1;<7 431;;; ;13<9 451;::çâôô+K@5, 318:< 31765 318:: 3169; 317<8 31749 317;< 3168<çâ�2+3, 31646 317;: 3157: 31398 3185: 3186< 31757 3143;çâ2ô+K@5, 31;:8 41684 31;:4 417<< 41544 41749 41558 41874çâô�+K@5, 41883 3196; 4189: 3174< 41549 3196; 414<8 31749çh 8159: 9138: 815;3 9176; 71:66 81:7; 71:67 91566

Dqdo|wlfdo/ Ordg +e, çx�+K, 041376 031845 041379 031678 041;<< 031;<5 041<86 03194<çx2+3, 415<8 518:; 41645 614;5 41;:3 519:9 41<64 6156;çxô+K@5, 41536 51559 41547 519;4 41:45 5164; 41:8: 51:68çâ��+3, 071;:4 051:84 071<38 051587 0:1;<7 061:76 0;145; 051<98çâ22+K, 81774 43158< 817;9 451693 :19:4 43194; :1;:3 45189:çâôô+K@5, 03173< 031888 031743 03194; 0317<8 0318:6 031834 03195<çâ�2+3, 31638 317:; 31577 31396 31856 31868 31757 31447çâ2ô+K@5, 31<:7 4177: 31<:4 418<7 41649 4184: 41663 41973çâô�+K@5, 41785 3187: 4179: 31663 4144< 3187: 413<8 31659çh 071486 06169: 071474 051<<6 071:66 061:66 071:67 061594

KVGW2H çxô+K@5, 413;; 0 0 0 4199: 0 0 51957çâ��+3, 0819:< 0 0 0 0;16;8 0 0 0614:4çâ22+K, 81838 0 0 0 ;16;8 0 0 461884çâ2ô+K@5, 513<8 0 0 0 61488 0 0 7178:

IVGW2H çxô+K@5, 4158: 0 0 0 41:8; 0 0 51:::çâ��+3, 061<44 0 0 0 0:148: 0 0 05179<çâ22+K, 81486 0 0 0 :148: 0 0 441<3:çâ2ô+K@5, 41<8; 0 0 0 51:5< 0 0 61<34

FOSW2H çxô+K@5, 3175< 0 0 0 41397 0 0 41:::çâ��+3, 071;33 0 0 0 0:148: 0 0 051736çâ22+K, 51<47 0 0 0 :148: 0 0 441;7<

95

Wdeoh 517= Glvsodfhphqwv dqg vwuhvvhv iru d vtxduh odplqdwh vxemhfwhg wr hljkw gl>huhqwerxqgdu| frqglwlrqv +Fdvh +4,/ O�2K@43/ N�@583 whupv,1

Wkhru| Yduldeoh E�E� E2E2 EôEô EeEe EDED ESES E.E. EHEHDqdo|wlfdo/ Ordg +d, çx�+K, 031<:9 0318:9 031<:: 0315<6 041::9 0413:< 041;39 031874

çx2+3, 31<66 51376 31<69 51<65 41:;5 515;3 41;54 61337çxô+K@5, 3197< 416;: 31984 41<:8 4155: 41883 41587 51359çâ��+3, 071986 051<74 071993 041;6; 0:1637 07175: 0:1765 051836çâ22+K, 61;;; ;1635 61;<: 441;45 :163< <1583 :1798 451433çâôô+K@5, 3197 317< 3197 316: 3183 3178 317< 3169çâ�2+3, 31554 31643 3153; 31385 317<: 31765 317:3 3144<çâ2ô+K@5, 31:46 41446 31:47 41756 4154< 415<5 41574 417<3çâô�+K@5, 418<5 31:<7 418<; 31694 41487 31:97 41463 316:7çh 719;7 <1637 719<6 451<98 71:66 ;15:; 71::< 4515:8

Dqdo|wlfdo/ Ordg +e, çx�+K, 031<:: 0318:< 031<:: 0315<: 041:;5 0413<3 041;45 03188:çx2+3, 31<58 51363 31<5: 51<46 41::9 515:3 41;48 51<;<çxô+K@5, 3197; 416;5 3197< 41<9: 4155: 4187: 41587 51353çâ��+3, 0719;4 051<:: 0719;; 041;;3 0:163< 071788 0:1769 051878çâ22+K, 61;:9 ;159< 61;;8 441:8< :1637 <1563 :1793 45138<çâôô+K@5, 03169 03184 03169 03196 03183 03187 03184 03197çâ�2+3, 3154< 3163; 3153: 31384 317<8 31763 3179< 31454çâ2ô+K@5, 31:76 41475 31:77 41783 4157< 41655 415:4 4184<çâô�+K@5, 41895 31:9; 4189: 3166: 41459 31:6; 41434 31683çh 071:84 031485 071:75 617;; 071:66 04154: 0719;; 51:7<

KVGW2H çxô+K@5, 3194: 0 0 0 41549 0 0 41<<5çâ��+3, 071<85 0 0 0 0:179; 0 0 051957çâ22+K, 61;36 0 0 0 :179; 0 0 4515<8çâ2ô+K@5, 41:58 0 0 0 614<3 0 0 717;<

IVGW2H çxô+K@5, 31989 0 0 0 4156: 0 0 5135;çâ��+3, 071783 0 0 0 0:148: 0 0 051775çâ22+K, 61:<< 0 0 0 :148: 0 0 441;;7çâ2ô+K@5, 41856 0 0 0 51:5< 0 0 61;;5

FOSW2H çxô+K@5, 3175< 0 0 0 41397 0 0 41:::çâ��+3, 071;33 0 0 0 0:148: 0 0 051736çâ22+K, 51<47 0 0 0 :148: 0 0 441;7<

96

Wdeoh 518= Glvsodfhphqwv dqg vwuhvvhv iru d vtxduh odplqdwh vxemhfwhg wr hljkw gl>huhqwerxqgdu| frqglwlrqv +Fdvh +5,/ N�@533 whupv,1

O�2K Yduldeoh E�E� E2E2 EôEô EeEe EDED ESES E.E. EHEH8 çx�+3, 3164< 31495 31654 313<3 31947 3155: 3195; 3143;

çx�+K, 031664 0314:8 031666 031436 031953 031566 031967 031447çx2+3, 41386 615;4 41394 8133: 41686 61645 416:9 81348çx2+K, 041377 0615:5 041384 071<<; 041679 061637 04169< 08133:çxô+K@5, 414;3 61836 414;; 815<: 41858 61875 41883 8163:çâ��+3, 07156: 05199: 071588 041<37 091<;: 06156: 0:1455 051379çâ��+K, 71839 51<68 71856 514:5 :14;3 61763 :1646 51568çâ22+K@6,W 061:59 0441665 061:86 04:1553 071:;7 0441775 071;97 04:157:çâ22+5K@6,W 618:7 4414:< 61933 4:139: 7196< 4415<: 71:4; 4:1434çâôô+K@5, 317<8 317<8 317<8 317<8 317<9 317<9 317<9 317<9çâ�2+3, 31589 3187; 31554 3137; 31737 318:; 31679 3138<çâ�2+K, 03158: 03187; 031556 031383 031736 0318:: 03167< 031394çâ2ô+K@5, 417:3 61<;3 417:; 81<38 41<44 71367 41<6< 81<4;çâô�+K@5, 513<6 4135; 51435 3178< 51986 41663 519:: 3194;çh 719<7 719<6 719<7 719<6 71:48 71:47 71:48 71:48

43 çx�+3, 3155: 31483 3155: 31395 31855 315:9 3185: 313:8çx�+K, 03155: 031483 03155: 031395 031853 0315:7 031858 0313:6çx2+3, 31798 5154: 31799 71:64 31:;5 515;5 31:<3 71:67çx2+K, 031793 051544 031794 071:58 031::: 0515:: 031:;8 071:5<çxô+K@5, 31779 513<3 3177: 7177< 31:86 51488 31:93 71786çâ��+3, 061334 0515;5 061336 04177: 081;<; 061836 081<85 041899çâ��+K, 61366 51647 61368 417:< 81<39 61844 81<8< 418:6çâ22+K@6,W 041:46 0;139< 041:49 04:14<7 051;;5 0;1648 051<3< 04:1538çâ22+5K@6,W 419:7 ;1363 419:9 4:1488 51;78 ;15:; 51;:4 4:149;çâôô+K@5, 3183 3183 3183 3183 3183 3183 3183 3183çâ�2+3, 31457 3153; 31454 31359 3159; 31597 31593 31365çâ�2+K, 031456 03153: 031454 031358 031599 031596 03158< 031364çâ2ô+K@5, 31:55 51;9; 31:56 81<88 4155; 51<<9 4156< 81<96çâô�+K@5, 61395 41<89 61397 3194; 61634 5147; 61643 319<7çh 71:47 71:47 71:47 71:47 71:5: 71:5: 71:5; 71:5;

Wydoxhv fruuhvsrqglqj wr wkh fhqwudo od|hu1

97

Wdeoh 519= Wkurxjk0wklfnqhvv glvsodfhphqw dqg vwuhvv glvwulexwlrqv iru d vtxduh odplqdwh+Fdvh +5,/ Frq?jxudwlrq E�E�c Ordg +d,/ O�2K@8/ N�@533 whupv,1

{ô@K çx� çx2 çxô çâ�� çâ22 çâôô çâ�2 çâ2ô çâô�3133 3164< 41386 41485 07156: 031843 031334 31589 31333 313333138 31534 31<5< 41488 051;44 031773 31345 31544 31456 419793143 3144; 31;46 4148; 041:65 0316:7 31376 314:9 3155: 5193<3148 3138: 31:37 41493 031;<7 031646 313;; 31479 31647 613:;3153 3133: 31933 41496 0314<; 031587 31474 31453 316;7 6155:3158 03136< 31833 41498 3177; 0314<; 314<; 313<7 31773 614343163 0313<4 31736 4149; 41454 031475 31587 3139: 317;5 51975+426,3 031465 3166< 4149< 4194< 031439 315<3 3137: 31834 51473+426,n 031465 3166< 4149< 31389 061:59 315<3 3137: 31834 514733168 03144: 31635 414:3 31388 061639 3163; 31375 319;; 514653173 0313:6 314<; 414:6 31384 051478 31699 3135; 41453 514463178 031363 31436 414:9 3137: 0413;: 3175< 31349 416:: 514333183 31345 31346 414;3 31376 0313;3 317<8 31337 417:3 513<63188 31386 0313:; 414;7 3136< 31<5< 31894 03133: 41737 513<63193 313<7 0314:6 414;; 31369 41<;; 31958 031353 414:7 514333198 31467 0315:: 414<6 31367 61485 319;6 031367 31:9: 51444+526,3 3147: 031648 414<7 31367 618:7 31:34 031373 318;< 51448+526,n 3147: 031648 414<7 0419<8 314<6 31:34 031373 318;< 5144831:3 31437 0316:9 414<; 04149< 3155< 31:6; 031393 31894 5199;31:8 3137< 0317:4 41536 03178; 315;7 31:<8 0313;: 3183; 614;331;3 31333 0318:5 4153; 31558 31675 31;87 031446 3176< 6167331;8 031386 0319:; 41546 31<97 31735 31<3< 031473 31689 6153;31<3 03144; 031:<4 4154; 41;85 31799 31<89 0314:4 31589 51:6731<8 031539 031<46 41556 51<<8 31867 31<;; 03153; 3146; 41:654133 031664 041377 4155: 71839 3193< 41334 03158: 31333 31333

98

Wdeoh 51:= Frqyhujhqfh vwxg| iru d krprjhqhrxv fr sodwh fodpshg rq doo hgjhv +Ordg +d,/O�*K@43/ O2*O�@318,1

N� çx�+K, çx2+K, çxô+K@5, çâ��+K, çâ22+K, çâôô+K@5, �â�2+K, �â2ô+K@5, çâô�+K@5, çh

58 ý3=3<4 6 ý3=5:6 8 3=497 < 4=643 3 3=666 4 3=7<8 : ý3=3:4 4 4=4:9 5 4=<;4 5 7=:4< 783 ý3=3<4 ; ý3=5:7 9 3=497 6 4=638 < 3=665 4 3=7<< 3 ý3=393 ; 4=4;8 ; 5=34; 5 7=::3 9

Wdeoh 51;= Glvsodfhphqw dqg vwuhvvhv iru d uhfwdqjxodu odplqdwh fodpshg rq doo hgjhv +Ordg+d,/ O�*K@8/ O2*O�@318/ N�@58 whupv,1

Fdvh çx�+K, çx2+K, çxô+K@5, çâ��+K, çâ22+5K@6,W �â�2+K, �â2ô+K@5, çâô�+K@5,5 03143 03166 3168 417< 41:8 0313: 5183 31976 03147 03155 3165 4143 3197 0417; 4195 31;5

Wydoxhv fruuhvsrqglqj wr wkh fhqwudo od|hu1

99

−10 −5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ11

/q0

x 3/H

x1/L

1 =0.05

x1/L

1 =0.1

x1/L

1 =0.3

x1/L

1 =0.5

Iljxuh 515= Qrupdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d vtxduh sodwh dw %2 'O2*2 +Fdvh+4,/ Frq?jxudwlrq E�E�/ Ordg +d,/ O�2K @ 8/ g�@583 whupv,1

9:

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ13

(0.05L1,0.5L

2,x

3)/(σ

13)max

x 3/H

B1B

1,(σ

13)max

= 1.798q0

B4B

4,(σ

13)max

= 0.211q0

B5B

5,(σ

13)max

= 1.590q0

B8B

8,(σ

13)max

= 0.216q0

Iljxuh 516= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq iru irxu gl>huhqw erxqgdu| frqglwlrqv +Fdvh+4,/ Ordg +d,/ O2@O�/ O�2K@8/ g�@583 whupv,1

9;

−1.25 −1 −0.75 −0.5 −0.25 0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ23

(0.05L1,0,x

3)/(σ

23)max

x 3/H

B1B

1,(σ

23)max

= 0.099q0

B2B

2,(σ

23)max

= 2.168q0

B3B

3,(σ

23)max

= 0.171q0

B5B

5,(σ

23)max

= 0.254q0


9<

−0.2 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ13

(0.05L1,0.5L

2,x

3)/(σ

13)max

x 3/H

B1B

1,(σ

13)max

= 1.811q0

B2B

2,(σ

13)max

= 0.510q0

B5B

5,(σ

13)max

= 1.453q0

B8B

8,(σ

13)max

= 0.252q0


:3

−0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ23

(0.05L1,0,x

3)/(σ

23)max

x 3/H

B1B

1,(σ

23)max

= 0.085q0

B5B

5,(σ

23)max

= 0.149q0

B6B

6,(σ

23)max

= 3.140q0

B7B

7,(σ

23)max

= −0.195q0


:4

−0.5 0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ33

(0.05L1,0.5L

2,x

3)/(q

0sin(0.05π)sin(0.5π))

x 3/H

B1B

1B

5B

5B

6B

6B

8B

8

Iljxuh 51:= Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq iru irxu gl>huhqw erxqgdu| frqglwlrqv +Fdvh+5,/ Ordg +d,/ O2@O�/ O�2K@8/ g�@533 whupv,1

:5

−0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σ13

/q0

x 3/H

x1/L

1 =0.04

x1/L

1 =0.08

x1/L

1 =0.12

x1/L

1 =0.16

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:6

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1

x2/L

2

10E T

[u3(x

1,x2,H

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0H

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wkh lqgh{1

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H = H 3

L

x1

(n ,n )1 3x3

(n ,n )3x1

(n ,n )x2

31

1

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L = 0(1) (N +1)1L = L

.

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.

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dqg rewdlqhg yhu| odujh vkhdulqj dqg wudqvyhuvh qrupdo vwuhvvhv dw wkh hgjhv ri wkh dfwxdwru1

[x dqg Qrru +4<<:, dovr vwxglhg d uhfwdqjxodu odplqdwhg sodwh zlwk dq dfwxdwru sdwfk e|

hpsor|lqj d suhglfwru0fruuhfwru ?qlwh hohphqw phwkrg exw glg qrw uhsruw wkh qdwxuh ri wkh

vwuhvvhv dw wkh hgjhv ri wkh sdwfk1 Wkh wkurxjk0wklfnqhvv glvwulexwlrq ri wkh wudqvyhuvh vkhdu

<:

vwuhvv dw irxu orfdwlrqv dorqj wkh vsdq ri wkh odplqd lv vkrzq lq Ilj1 61631 Dv h{shfwhg/ wkh

wudqvyhuvh vkhdu vwuhvv lv odujh rq wkh lqwhuidfh ehwzhhq wkh S]W dqg wkh vxevwudwh1

Wkh glvwulexwlrqv ri wkh wudqvyhuvh glvsodfhphqw rq wkuhh krul}rqwdo sodqhv ri wkh vxevwudwh/

ghslfwhg lq Ilj1 6164/ vkrz wkh lqwhqvh wudqvyhuvh horqjdwlrq ri wkh qrupdov dw wkh fruqhuv

ri wkh S]W0vxevwudwh lqwhuidfh1 Wkh wudqvyhuvh horqjdwlrq ri wkh qrupdov lv qhjoljleoh lq

wkh ylflqlw| ri wkh fodpshg dqg iuhh hgjhv ri wkh vxevwudwh1 Wkhvh uhvxowv lqglfdwh wkdw

lw lv lpsruwdqw wr lqfrusrudwh wudqvyhuvh horqjdwlrq ri qrupdov lqwr wzr0glphqvlrqdo sodwh

wkhrulhv lq rughu wr fdswxuh wkh h{dfw qdwxuh ri wkh vwuhvvhv dw wkh hgjhv ri wkh S]W sdwfk1

619 Frqfoxvlrqv

Zh kdyh h{whqghg wkh Hvkhoe|0Vwurk irupdolvp wr vwxg| wkh jhqhudol}hg sodqh ghirupdwlrqv

ri d olqhdu slh}rwkhuprhodvwlf odplqdwhg sodwh1 Wkh wkuhh glphqvlrqdo htxloleulxp htxdwlrqv

duh h{dfwo| vdwlv?hg dw hyhu| srlqw ri wkh erg|1 Krzhyhu/ wkh erxqgdu| dqg lqwhuidfh frq0

wlqxlw| frqglwlrqv duh vdwlv?hg lq wkh vhqvh ri Irxulhu vhulhv1 E| nhhslqj d odujh qxpehu

ri whupv lq wkh vhulhv vroxwlrqv/ glvsodfhphqwv dqg vwuhvvhv fdq eh frpsxwhg wr dq| ghvluhg

ghjuhh ri dffxudf|1 Zh kdyh frpsxwhg wkhupdo vwuhvvhv lq d odplqdwhg judsklwh0hsr{| sodwh

zlwk hgjhv vxemhfwhg wr gl>huhqw w|shv ri erxqgdu| frqglwlrqv1 Zh kdyh dovr vwxglhg ghiru0

pdwlrqv ri d f*bf*f judsklwh0hsr{| sodwh zlwk d S]W08D od|hu erqghg wr lwv xsshu vxuidfh

dqg wkh frpsrvlwh odplqdwh ordghg hlwkhu e| dq hohfwulf srwhqwldo ru d whpshudwxuh glvwul0

exwlrq ru vxuidfh wudfwlrqv dssolhg wr wkh wrs0prvw vxuidfh zlwk wkh erwwrp0prvw vxuidfh

xqordghg1 Wkh h>hfw ri hlwkhu fodpslqj wkh hgjhv/ vlpso| vxssruwlqj wkhp ru kdylqj wkhp

wudfwlrq iuhh kdv dovr ehhq gholqhdwhg1 Zh dovr dqdo|}hg ghirupdwlrqv dqg vwuhvvhv lq d

judsklwh0hsr{| fdqwlohyhu ehdp zlwk d wklq S]W0sdwfk erqghg wr lwv xsshu vxuidfh dw wkh

fhqwhu ri wkh ehdp1 Dv looxvwudwhg e| wkh uhvxowv/ wkh phwkrg lv yhuvdwloh dqg fdsdeoh ri

dqdo|}lqj slh}rwkhuprhodvwlf sodwhv vxemhfwhg wr duelwudu| erxqgdu| frqglwlrqv rq wkh hgjhv

<;

dqg wkh wrs dqg erwwrp orqj idfhv1

Zkhq d slh}rhohfwulf dfwxdwru sdwfk lv dwwdfkhg wr dq hodvwlf fdqwlohyhu sodwh/ wkh vkhdu

dqg wudqvyhuvh qrupdo vwuhvvhv duh yhu| odujh dw wkh hgjhv ri wkh lqwhuidfh1 Wkh wudqvyhuvh

horqjdwlrq ri wkh qrupdov lv dovr vxevwdqwldo dw wkhvh srlqwv1

<<

61: Uhihuhqfhv

K1 Dooln dqg W1 M1 U1 Kxjkhv1 Ilqlwh hohphqw phwkrg iru slh}rhohfwulf yleudwlrq1 Lqwhuqd0

wlrqdo Mrxuqdo iru Qxphulfdo Phwkrgv lq Hqjlqhhulqj/ 5=484848:/ 4<:31

W1 Edloh| dqg M1 H1 Kxeedug1 Glvwulexwhg slh}rhohfwulf0sro|phu dfwlyh yleudwlrq frqwuro ri

d fdqwlohyhu ehdp1 Mrxuqdo ri Jxlgdqfh/ Frqwuro/ dqg G|qdplfv/ ;=9388944/ 4<;81

U1 F1 Edwud dqg [1 T1 Oldqj1 Vkdsh frqwuro ri yleudwlqj vlpso| vxssruwhg uhfwdqjxodu

sodwhv1 DLDD Mrxuqdo/ 67=4490455/4<<91

U1 F1 Edwud dqg [1 T1 Oldqj1 Ilqlwh g|qdplf ghirupdwlrqv ri vpduw vwuxfwxuhv1 Frpsxwd0

wlrqdo Phfkdqlfv/ 53=75:876;/ 4<<:1

V1 Eurrnv dqg S1 Kh|olqjhu1 Vwdwlf ehkdylru ri slh}rhohfwulf odplqdwhv zlwk glvwulexwhg dqg

sdwfkhg dfwxdwruv1 Mrxuqdo ri Lqwhooljhqw Pdwhuldo V|vwhpv dqg Vwuxfwxuhv/ 8=9688979/

4<<71

H1 I1 Fudzoh| dqg M1 gh Oxlv1 Xvh ri slh}rhohfwulf dfwxdwruv dv hohphqwv ri lqwhooljhqw

vwuxfwxuhv1 DLDD Mrxuqdo/ 58=46:6846;8/ 4<;:1

J1 S1 Gxeh/ V1 Ndsxuld dqg S1 F1 Gxplu1 H{dfw slh}rwkhuprhodvwlf vroxwlrq ri vlpso|0

vxssruwhg ruwkrwurslf dw sdqho lq f|olqgulfdo ehqglqj1 Lqwhuqdwlrqdo Mrxuqdo ri Ph0

fkdqlfdo Vflhqfhv/ 6;+44,=4494844::/ 4<<91

J1 S1 Gxeh/ P1 P1 Xsdgk|d|/ S1 F1 Gxplu dqg V1 Nxpdu1 Slh}rwkhuprhodvwlf vroxwlrq iru

dqjoh0so| odplqdwhg sodwh lq f|olqgulfdo ehqglqj1 Vwuxfwxudo Hqjlqhhulqj dqg Phfkdq0

lfv/ 9+8,=85<8875/ 4<<;1

M1 G1 Hvkhoe|/ Z1 W1 Uhdg dqg Z1 Vkrfnoh|1 Dqlvrwurslf hodvwlflw| zlwk dssolfdwlrqv wr

glvorfdwlrq wkhru|1 Dfwd Phwdooxujlfd/ 4=584858</ 4<861

433

V1 N1 Kd/ F1 Nhlohuv dqg I1 N1 Fkdqj1 Ilqlwh hohphqw dqdo|vlv ri frpsrvlwh vwuxfwxuhv

frqwdlqlqj slh}rfhudplf vhqvruv dqg dfwxdwruv1 DLDD Mrxuqdo/ 63=::58:;3/ 4<<51

G1 Lhvdq1 Rq vrph wkhruhpv lq wkhuprslh}rhohfwulflw|1 Mrxuqdo ri Wkhupdo Vwuhvvhv/

45+5,=53<8556/ 4<;<1

V1 Lp dqg V1 Q1 Dwoxul1 H>hfwv ri d slh}r0dfwxdwru rq d ?qlwho| ghiruphg ehdp vxemhfwhg

wr jhqhudo ordglqj1 DLDD Mrxuqdo/ 5:=4;3484;3:/ 4<;<1

N1 G1 Mrqqdodjdggd/ J1 H1 Eodqgirug dqg W1 U1 Wdxfkhuw1 Slh}rwkhuprhodvwlf frpsrvlwh

sodwh dqdo|vlv xvlqj ?uvw0rughu vkhdu0ghirupdwlrq wkhru|1 Frpsxwhuv dqg Vwuxfwxuhv/

84=:<8;</ 4<<71

V1 Ndsxuld/ J1 S1 Gxeh dqg S1 F1 Gxplu1 H{dfw slh}rwkhuprhodvwlf vroxwlrq iru vlp0

so| vxssruwhg odplqdwhg dw sdqho lq f|olqgulfdo ehqglqj1 ]hlwvfkuliw ixu dqjhzdqgwh

Pdwkhpdwln xqg Phfkdqln/ ::+7,=5;485<6/ 4<<:1

F1 N1 Ohh1 Wkhru| ri odplqdwhg slh}rhohfwulf sodwhv iru wkh ghvljq ri glvwulexwhg vhq0

vruv2dfwxdwruv1 sduw 4= jryhuqlqj htxdwlrqv dqg uhflsurfdo uhodwlrqvklsv1 Mrxuqdo ri

wkh Dfrxvwlf Vrflhw| ri Dphulfd/ ;:=44778448;/ 4<<31

U1 G1 Plqgolq1 Rq wkh htxdwlrqv ri prwlrq ri slh}rhohfwulf fu|vwdov1 Sureohpv ri Frqwlqxxp

Phfkdqlfv/ Q1 L1 Pxvnkholvkylol :3wk Eluwkgd| Yroxph/ VLDP/ Sklodghoskld/ ss1 5;50

5<3/ 4<941

U1 G1 Plqgolq1 Htxdwlrqv ri kljk iuhtxhqf| yleudwlrqv ri wkhuprslh}rhohfwulf fu|vwdo sodwhv1

Lqwhuqdwlrqdo Mrxuqdo ri Vrolgv dqg Vwuxfwxuhv/ 43=9588965/ 4<:71

M1 D1 Plwfkhoo dqg M1 Q1 Uhgg|1 D uh?qhg k|eulg sodwh wkhru| iru frpsrvlwh odplqdwhv zlwk

slh}rhohfwulf odplqdh1 Lqwhuqdwlrqdo Mrxuqdo ri Vrolgv dqg Vwuxfwxuhv/ 65+49,=56788

569:/ 4<<81

434

G1 K1 Proohqkdxhu dqg R1 K1 Jul!q Mu1 Lqgxfhg vwudlq ri dfwxdwlrq ri vxuidfh erqghg

slh}rfhudplf sdwfkhv= D qxphulfdo dqg h{shulphqwdo vwxg|1 Mrxuqdo ri Lqwhooljhqw

Pdwhuldo V|vwhpv dqg Vwuxfwxuhv/ 8=6888695/ 4<<71

Z1 Qrzdfnl1 Vrph jhqhudo wkhruhpv ri wkhuprslh}rhohfwulflw|1 Mrxuqdo ri Wkhupdo Vwuhvvhv/

4+5,=4:484;5/ 4<:;1

M1 O1 Qrzlqvnl1 Wkhru| ri Wkhuprhodvwlflw| zlwk Dssolfdwlrqv1 Vlmwkr> dqg Qrrugkr>

Lqwhuqdwlrqdo Sxeolvkhuv E1 Y1/ Doskhq ddq ghq Ulmq/ wkh Qhwkhuodqgv/ 4<:;1

Q1 M1 Sdjdqr1 H{dfw vroxwlrqv iru frpsrvlwh odplqdwhv lq f|olqgulfdo ehqglqj1 Mrxuqdo ri

Frpsrvlwh Pdwhuldov/ 6=6<;8744/ Mxo| 4<9<1

Q1 M1 Sdjdqr1 H{dfw vroxwlrqv iru uhfwdqjxodu elgluhfwlrqdo frpsrvlwhv dqg vdqgzlfk sodwhv1

Mrxuqdo ri Frpsrvlwh Pdwhuldov/ 7=53867/ 4<:31

V1 V1 Udr dqg P1 Vxqdu1 Dqdo|vlv ri glvwulexwhg wkhuprslh}rhohfwulf vhqvruv dqg dfwxdwruv

lq dgydqfhg lqwhooljhqw vwuxfwxuhv1 DLDD Mrxuqdo/ 64+:,=45;3845;9/ 4<<61

P1 F1 Ud|/ N1 P1 Udr dqg E1 Vdpdqwd1 H{dfw dqdo|vlv ri frxsohg hohfwurhodvwlf ehkdylru

ri slh}rhohfwulf sodwh xqghu f|olqgulfdo ehqglqj1 Frpsxwhuv dqg Vwuxfwxuhv/ 78+7,=99:8

9::/ 4<<51

P1 F1 Ud|/ U1 Ekdwwdfkdu|d dqg E1 Vdpdqwd1 H{dfw vroxwlrqv iru vwdwlf dqdo|vlv ri lqwhool0

jhqw vwuxfwxuhv1 DLDD Mrxuqdo/ 64+<,=49;7849<4/ 4<<61

G1 K1 Ureelqv dqg M1 Q1 Uhgg|1 Dqdo|vlv ri slh}rhohfwulfdoo| dfwxdwhg ehdpv xvlqj d

od|hu0zlvh glvsodfhphqw wkhru|1 Frpsxwhuv dqg Vwuxfwxuhv/ 74=59885:</ 4<<41

G1 K1 Ureelqv dqg M1 Q1 Uhgg|1 Dq h!flhqw frpsxwdwlrqdo prgho iru wkh vwuhvv dqdo|vlv

ri vpduw sodwh vwuxfwxuhv1 Vpduw Pdwhuldov dqg Vwuxfwxuhv/ 8=6868693/ 4<<91

435

I1 Vkdqj/ ]1 Zdqj dqg ]1 Ol1 Dqdo|vlv ri wkhupdoo| lqgxfhg f|olqgulfdo h{xuh ri odplqdwhg

sodwhv zlwk slh}rhohfwulf od|huv1 Frpsrvlwhv Sduw E/ 5;E=4;884<6/ 4<<:1

D1 Q1 Vwurk1 Glvorfdwlrqv dqg fudfnv lq dqlvrwurslf hodvwlflw|1 Sklorvrsklfdo Pdjd}lqh/

6=9588979/ 4<8;1

\1 \1 Wdqj/ D1 N1 Qrru dqg N1 [x1 Dvvhvphqw ri frpsxwdwlrqdo prghov iru wkhuprhohf0

wurhodvwlf pxowlod|huhg sodwhv1 Frpsxwhuv dqg Vwuxfwxuhv/ 94+8,=<488<66/ 4<<91

\1 \1 Wdqj dqg N1 [x1 G|qdplf dqdo|vlv ri d slh}rwkhuprhodvwlf odplqdwhg sodwh1 Mrxuqdo

ri Wkhupdo Vwuhvvhv/ 4;=;:8437/ 4<<81

W1 U1 Wdxfkhuw1 Slh}rwkhuprhodvwlf ehkdylru ri d odplqdwhg sodwh1 Mrxuqdo ri Wkhupdo

Vwuhvvhv/ 48=5886:/ 4<<51

W1 F1 W1 Wlqj1 Dqlvrwurslf Hodvwlflw|1 Wkhru| dqg Dssolfdwlrqv1 R{irug Hqjlqhhulqj

Vflhqfh Vhulhv/ Qr 781 R{irug Xqly Suhvv/ Qhz \run/ 4<<91

K1 V1 W}rx dqg U1 \h1 Slh}rwkhuprhodvwlflw| dqg suhflvlrq frqwuro ri slh}rhohfwulf v|vwhpv=

wkhru| dqg ?qlwh hohphqwv dqdo|vlv1 Mrxuqdo ri Yleudwlrq dqg Dfrxvwlfv/ 449=7;<87<8/

4<<71

E1 W1 Zdqj dqg F1 D1 Urjhuv1 Odplqdwh sodwh wkhru| iru vsdwldoo| glvwulexwhg lqgxfhg

vwudlq dfwxdwruv1 Mrxuqdo ri Frpsrvlwh Pdwhuldov/ 58=7668785/ 4<<41

N1 [x dqg D1 N1 Qrru1 Suhglfwru0fruuhfwru ?qlwh hohphqw dssurdfk iru hohfwurhodvwlf dqdo|vlv

ri k|eulg frpsrvlwh sodwhv1 Frpsxwhu Phwkrgv lq Dssolhg Phfkdqlfv dqg Hqjlqhhulqj/

47:=46<8478/ 4<<:1

N1 [x/ D1 N1 Qrru dqg \1 \1 Wdqj1 Wkuhh0glphqvlrqdo vroxwlrqv iru frxsohg wkhuprhohf0

wurhodvwlf uhvsrqvh ri pxowlod|huhg sodwhv 1 Frpsxwhu Phwkrgv lq Dssolhg Phfkdqlfv

dqg Hqjlqhhulqj/ 459=68886:4/ 4<<81

436

M1 V1 \dqj/ U1 F1 Edwud dqg [1 T1 Oldqj1 Wkh f|olqgulfdo ehqglqj yleudwlrq ri d odplqdwhg

hodvwlf sodwh gxh wr slh}rhohfwulf dfwxdwruv1 Vpduw Pdwhuldov dqg Vwuxfwxuhv/ 6=7;887<6/

4<<71

M1 V1 \dqj dqg K1 I1 Wlhuvwhq1 Hodvwlf dqdo|vlv ri wkh wudqvihu ri vkhdulqj vwuhvv iurp

sduwldoo| hohfwurghg slh}rhohfwulf dfwxdwruv wr frpsrvlwh sodwhv lq f|olqgulfdo ehqglqj1

Vpduw Pdwhuldov dqg Vwuxfwxuhv/ 9=6660673/ 4<<:

[1 [1 \dqj/ V1 Vkhq dqg ]1 E1 Nxdqj1 Wkh ghjhqhudwh vroxwlrq iru slh}rwkhuprhodvwlf

pdwhuldov1 Hxurshdq Mrxuqdo ri Phfkdqlfv/ D/ Vrolgv/ 49+8,=::<84<6/ 4<<:1

\1 V1 ]krx dqg K1 I1 Wlhuvwhq1 Dq hodvwlf dqdo|vlv ri odplqdwhg sodwhv lq f|olqgulfdo ehqglqj

gxh wr slh}rhohfwulf dfwxdwruv1 Vpduw Pdwhuldov dqg Vwuxfwxuhv/ 6=5888598/ 4<<71

437

−0.5 −0.25 0 0.25 0.5

0.25

0.5

0.75

1

σ11

/αTE

TT

0

x 3/H

x1/L =0.1

x1/L =0.3

x1/L =0.4

x1/L =0.5

Iljxuh 616= Orqjlwxglqdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv iru d fodpshg0fodpshg ^32<3òdplqdwh +u*M @8,

438

−0.06 −0.03 0 0.03 0.06 0.09

0.25

0.5

0.75

1

σ13

/αTE

TT

0

x 3/H

x1/L =0.1

x1/L =0.4

x1/L =0.6

x1/L =0.9

Iljxuh 617= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3` 77 odplqdwh+u*M @8,

439

−0.04 −0.02 0 0.02 0.04 0.06

0.25

0.5

0.75

1

σ13

/αTE

TT

0

x 3/H

x1/L =0.1

x1/L =0.4

x1/L =0.6

x1/L =0.9

Iljxuh 618= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3` ä7 odplqdwh+u*M @8,

43:

0.25 0.5 0.75 1

−0.05

−0.025

0

0.025

0.05

0.075

σ 13/α

TE

TT

0

x1/L

x3/H =0.5−

x3/H =0.5+

x3/H =0.25

x3/H =0.75

Iljxuh 619= Wudqvyhuvh vkhdu vwuhvv yduldwlrqv rq irxu sodqhv iru d ^32<3` 77 odplqdwh +u*M@8,

43;

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

σ 13/α

TE

TT

0

x1/L

x3/H =0.5−

x3/H =0.5+

x3/H =0.25

x3/H =0.75

Iljxuh 61:= Wudqvyhuvh vkhdu vwuhvv yduldwlrqv rq irxu sodqhv iru d ^32<3` ä8 odplqdwh +u*M@8,

43<

−6 −5 −4 −3 −2 −1 0 1 20

0.3

0.6

0.9

1

σ13

L/ETd

Tφ

0

x 3/H

x1/L =0.05

x1/L =0.2

x1/L =0.3

x1/L =0.4

Iljxuh 61;= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` 77odplqdwh1 Ordg Fdvh +d, +u*M @8,1

443

−0.02 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 0.02 0.0250

0.3

0.6

0.9

1

σ13

/αTE

TT

0

x 3/H

x1/L =0.05

x1/L =0.2

x1/L =0.3

x1/L =0.4

Iljxuh 61<= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` 77odplqdwh1 Ordg Fdvh +e, +u*M @8,1

444

−0.5 0 0.5 1 1.5 20

0.3

0.6

0.9

1

σ13

/q0

x 3/H

x1/L =0.05

x1/L =0.2

x1/L =0.3

x1/L =0.4

Iljxuh 6143= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` 77odplqdwh1 Ordg Fdvh +f, +u*M @8,1

445

−4 −3 −2 −1 0 1 2 3 4 5 60

0.3

0.6

0.9

1

σ13

L/ETd

Tφ

0

x 3/H

x1/L =0.05

x1/L =0.4

x1/L =0.6

x1/L =0.95

Iljxuh 6144= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +d, +u*M @8,1

446

−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.040

0.3

0.6

0.9

1

σ13

/αTE

TT

0

x 3/H

x1/L =0.05

x1/L =0.4

x1/L =0.6

x1/L =0.95

Iljxuh 6145= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +e, +u*M @8,1

447

−1 0 1 2 3 4 5 60

0.3

0.6

0.9

1

σ13

/q0

x 3/H

x1/L =0.05

x1/L =0.4

x1/L =0.6

x1/L =0.95

Iljxuh 6146= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +f, +u*M @8,1

448

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−5

0

5

10

15

σ 31L/

ETd T

φ 0

x1/L

x3/H =0.3

x3/H =0.5

x3/H =0.6

x3/H =0.9

Iljxuh 6147= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu sodqhv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +d, +u*M @8,1

449

0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1−4

−3

−2

−1

0

1

2

3

4

5

6

σ 31L/

ETd T

φ 0

x1/L

x3/H =0.3

x3/H =0.5

x3/H =0.6

x3/H =0.9

Iljxuh 6148= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu sodqhv ri d ^32<3232S]W` ä8odplqdwh forvh wr wkh iuhh hgjh1 Ordg Fdvh +d, +u*M @8,1

44:

−6 −5 −4 −3 −2 −1 0

x 10−5

0.9

0.925

0.95

0.975

1

φdT/Lα

TT

0

x 3/H

x1/L =0.05

x1/L =0.4

x1/L =0.6

x1/L =0.95

Iljxuh 6149= Hohfwulf srwhqwldo lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +e, +u*M @8,1

44;

−25 −20 −15 −10 −5 0 5

x 10−4

0.9

0.925

0.95

0.975

1

φdTE

T/Lq

0

x 3/H

x1/L =0.05

x1/L =0.4

x1/L =0.6

x1/L =0.95

Iljxuh 614:= Hohfwulf srwhqwldo lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +f, +u*M @8,1

44<

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50.9

0.925

0.95

0.975

1

D3/E

Td

Tα

TT

0

x 3/H

x1/L =0.05

x1/L =0.3

x1/L =0.7

x1/L =0.95

Iljxuh 614;= Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +e, +u*M @8,1

453

−2 0 2 4 6 8 10 12 14 16 18 200.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

D3/d

Tq

0

x 3/H

x1/L =0.05

x1/L =0.3

x1/L =0.7

x1/L =0.95

Iljxuh 614<= Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +f, +u*M @8,1

454

−0.01 0 0.01 0.02 0.03 0.04 0.050.9

0.925

0.95

0.975

1

D1/E

Td

Tα

TT

0

x 3/H

x1/L =0.05

x1/L =0.3

x1/L =0.7

x1/L =0.95

Iljxuh 6153= Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +e, +u*M @8,1

455

−1 0 1 2 3 4 5 6 70.9

0.925

0.95

0.975

1

D1/d

Tq

0

x 3/H

x1/L =0.05

x1/L =0.3

x1/L =0.7

x1/L =0.95

Iljxuh 6154= Hohfwulf glvsodfhphqw lqgxfhg lq S]W dw irxu vhfwlrqv ri d ^32<3232S]W` ä8odplqdwh1 Ordg Fdvh +f, +u*M @8,1

456

−2 −1 0 1 2 3 4 50

0.3

0.6

0.9

1

u1/d

Tφ

0

x 3/H

x1/L =0.05

x1/L =0.3

x1/L =0.7

x1/L =0.95

Iljxuh 6155= Glvwulexwlrq ri wkh phfkdqlfdo d{ldo glvsodfhphqw rq irxu vhfwlrqv ri d^32<3232S]W` ä8 odplqdwh1 Ordg Fdvh +d, +u*M @8,1

457

−0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350

0.3

0.6

0.9

1

u1/Lα

TT

0

x 3/H

x1/L =0.05

x1/L =0.3

x1/L =0.7

x1/L =0.95

Iljxuh 6156= Glvwulexwlrq ri wkh phfkdqlfdo d{ldo glvsodfhphqw rq irxu vhfwlrqv ri d^32<3232S]W` ä8 odplqdwh1 Ordg Fdvh +e, +u*M @8,1

458

−15 −10 −5 0 5 10 150

0.3

0.6

0.9

1

σ11

/q0

x 3/H

x1/L =0.1

x1/L =0.25

x1/L =0.4

x1/L =0.5

Iljxuh 6157= Orqjlwxglqdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` ää odpl0qdwh1 Ordg Fdvh +f, +u*M @8,1

459

−100 −80 −60 −40 −20 0 20 400

0.3

0.6

0.9

1

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L/ETd

Tφ

0

x 3/H

x1/L =0.1

x1/L =0.25

x1/L =0.4

x1/L =0.5

Iljxuh 6158= Orqjlwxglqdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` ää odpl0qdwh1 Ordg Fdvh +d, +u*M @8,1

45:

0 0.1 0.2 0.3 0.4 0.50

0.3

0.6

0.9

1

σ33

L/ETd

Tφ

0

x 3/H

x1/L =0.1

x1/L =0.25

x1/L =0.4

x1/L =0.5

Iljxuh 6159= Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` 77odplqdwh1 Ordg Fdvh +d, +u*M @8,1

45;

−3 −2.5 −2 −1.5 −1 −0.5 0 0.5

x 10−3

0

0.3

0.6

0.9

1

σ33

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TT

0

x 3/H

x1/L =0.1

x1/L =0.25

x1/L =0.4

x1/L =0.5

Iljxuh 615:= Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d ^32<3232S]W` 77odplqdwh1 Ordg Fdvh +e, +u*M @8,1

45<

0 0.25 0.5 0.75 1−80

−60

−40

−20

0

20

40

60

80

σ 13L/

ETd T

φ 0

x1/L

x3/H =5/12

x3/H =10/12

x3/H =11/12

Iljxuh 615;= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq wkuhh sodqhv vhfwlrqv ri d fdqwlohyhuodplqdwh zlwk d S]W sdwfk

463

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−20

0

20

40

60

80

100

120

140

σ 33L/

ETd T

φ 0

x1/L

x3/H =5/12

x3/H =10/12

x3/H =11/12

Iljxuh 615<= Wudqvyhuvh qrupdo vwuhvv glvwulexwlrq rq wkuhh sodqhv vhfwlrqv ri d fdqwlohyhuodplqdwh zlwk d S]W sdwfk

464

−10 −8 −6 −4 −2 0 2 4 6 8 10 120

5/12

10/12

1

σ13

L/ETd

Tφ

0

x 3/H

x1/L =0.15

x1/L =0.3

x1/L =0.7

x1/L =0.85

Iljxuh 6163= Wudqvyhuvh vkhdu vwuhvv glvwulexwlrq rq irxu vhfwlrqv ri d fdqwlohyhu odplqdwhzlwk d S]W sdwfk

465

0 0.25 0.5 0.75 1

0

5

10

15

20

25

u 3/dTφ 0

x1/L

x3/H =0

x3/H =5/12

x3/H =10/12

Iljxuh 6164= Wudqvyhuvh glvsodfhphqw rq wkuhh sodqhv ri d fdqwlohyhu odplqdwh zlwk d S]Wsdwfk

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