Commit 1c154f4eaeac404e737204e4fb04edb8af1ff438
- Diff rendering mode:
- inline
- side by side
Harjoitustyo/JY1_Harjoitustyo.lyx
(307 / 12)
  | |||
309 | 309 | \begin_layout Standard | |
310 | 310 | Darcyn laki on muotoa | |
311 | 311 | \begin_inset Formula \begin{equation} | |
312 | \phi v=-\frac{\kappa}{\mu}\nabla p\,,\label{eq:Darcy}\end{equation} | ||
312 | v_{s}:=\phi v=-\frac{\kappa}{\mu}\nabla p\,,\label{eq:Darcy}\end{equation} | ||
313 | 313 | ||
314 | 314 | \end_inset | |
315 | 315 | ||
… | … | ||
341 | 341 | \begin_inset Formula $v$ | |
342 | 342 | \end_inset | |
343 | 343 | ||
344 | nesteen virtausnopeus ja | ||
344 | nesteen virtausnopeus (ilman väliainetta) ja | ||
345 | 345 | \begin_inset Formula $p$ | |
346 | 346 | \end_inset | |
347 | 347 | ||
348 | 348 | paine. | |
349 | |||
350 | \begin_inset Formula $v_{s}$ | ||
351 | \end_inset | ||
352 | |||
353 | :llä merkitään nk. | ||
354 | efektiivistä nopeutta. | ||
349 | 355 | Jotta malli olisi ratkaistavissa tarvitaan jokin muu ehto muuttujille | |
350 | 356 | \begin_inset Formula $v$ | |
351 | 357 | \end_inset | |
… | … | ||
382 | 382 | ulottuvuudessa. | |
383 | 383 | Tällöin saadaan | |
384 | 384 | \begin_inset Formula \begin{gather} | |
385 | \phi v=-\frac{\kappa}{\mu}p_{,x}\,,\nonumber \\ | ||
385 | v_{s}=\phi v=-\frac{\kappa}{\mu}p_{,x}\,,\nonumber \\ | ||
386 | 386 | \rho_{,t}+\rho_{,x}v+\rho v_{,x}\,.\label{eq:1dModel}\end{gather} | |
387 | 387 | ||
388 | 388 | \end_inset | |
… | … | ||
431 | 431 | \begin_inset Formula $v$ | |
432 | 432 | \end_inset | |
433 | 433 | ||
434 | :n lauseke massan säilymislain yhtälöön. | ||
434 | :n lauseke massan säilymislain yhtälöön mallissa | ||
435 | \begin_inset CommandInset ref | ||
436 | LatexCommand ref | ||
437 | reference "eq:1dModel" | ||
438 | |||
439 | \end_inset | ||
440 | |||
441 | . | ||
435 | 442 | Oletetaan, että huokoinen aine ei ole täysin tiivis, jolloin | |
436 | 443 | \begin_inset Formula $\phi>0$ | |
437 | 444 | \end_inset | |
… | … | ||
449 | 449 | \end_inset | |
450 | 450 | ||
451 | 451 | :llä voidaan jakaa. | |
452 | Lisäksi oletettiin, että viskositeetti | ||
452 | Lisäksi oletetaan, että viskositeetti | ||
453 | 453 | \begin_inset Formula $\mu$ | |
454 | 454 | \end_inset | |
455 | 455 | ||
456 | on vakio. | ||
456 | ja permeabiliteetti | ||
457 | \begin_inset Formula $\kappa$ | ||
458 | \end_inset | ||
459 | |||
460 | (väliaineelle ominainen vastus) ovat vakioita. | ||
457 | 461 | Saadaan | |
462 | \begin_inset Formula \[ | ||
463 | \rho_{,t}+\rho_{,x}\left(-\frac{\kappa}{\mu}\frac{1}{\phi}p_{,x}\right)+\rho\left[(-\frac{\kappa}{\mu}\frac{1}{\phi}p_{,x})_{,x}\right]=0\,,\] | ||
464 | |||
465 | \end_inset | ||
466 | |||
467 | mistä edelleen | ||
458 | 468 | \begin_inset Formula \begin{equation} | |
459 | \rho_{,t}-\frac{1}{\mu}\frac{\kappa}{\phi}\rho_{,x}p_{,x}-\frac{\rho}{\mu}\left[(\frac{\kappa}{\phi})_{,x}p_{,x}+\frac{\kappa}{\phi}p_{,xx}\right]=0\,.\label{eq:1dTogether}\end{equation} | ||
469 | \rho_{,t}-\frac{\kappa}{\mu}\frac{1}{\phi}\rho_{,x}p_{,x}-\rho\frac{\kappa}{\mu}\left[-\frac{1}{\phi^{2}}\phi_{,x}p_{,x}+\frac{1}{\phi}p_{,xx}\right]=0\,.\label{eq:1dTogether}\end{equation} | ||
460 | 470 | ||
461 | 471 | \end_inset | |
462 | 472 | ||
473 | Kertomalla puolittain funktiolla | ||
474 | \begin_inset Formula $\phi$ | ||
475 | \end_inset | ||
476 | |||
477 | ja vakiolla | ||
478 | \begin_inset Formula $\frac{\mu}{\kappa}$ | ||
479 | \end_inset | ||
480 | |||
481 | saadaan lopulta | ||
482 | \begin_inset Formula \begin{equation} | ||
483 | \frac{\mu}{\kappa}\phi^{2}\rho_{,t}-\phi\rho_{,x}p_{,x}+\phi_{,x}\rho p_{,x}-\phi\rho p_{,xx}=0\,.\label{eq:1dTogether2}\end{equation} | ||
484 | |||
485 | \end_inset | ||
486 | |||
463 | 487 | Lisätään nyt yhtälöön | |
464 | 488 | \begin_inset CommandInset ref | |
465 | 489 | LatexCommand eqref | |
466 | reference "eq:1dTogether" | ||
490 | reference "eq:1dTogether2" | ||
467 | 491 | ||
468 | 492 | \end_inset | |
469 | 493 | ||
… | … | ||
501 | 501 | . | |
502 | 502 | Tällöin | |
503 | 503 | \begin_inset Formula \[ | |
504 | \beta\rho p_{,t}-\frac{1}{\mu}\frac{\kappa}{\phi}\beta\rho(p_{,x})^{2}-\frac{\rho}{\mu}\left[(\frac{\kappa}{\phi})_{,x}p_{,x}+\frac{\kappa}{\phi}p_{,xx}\right]=0\,.\] | ||
504 | \frac{\mu}{\kappa}\beta\phi^{2}\rho p_{,t}-\beta\rho\phi(p_{,x})^{2}+\phi_{,x}\rho p_{,x}-\phi\rho p_{,xx}=0\,.\] | ||
505 | 505 | ||
506 | 506 | \end_inset | |
507 | 507 | ||
508 | Yhtäpitävästi | ||
509 | \begin_inset Formula \[ | ||
510 | p_{,t}-\frac{1}{\mu}\frac{\kappa}{\phi}(p_{,x})^{2}-\frac{1}{\beta\mu}\left[(\frac{\kappa}{\phi})_{,x}p_{,x}+\frac{\kappa}{\phi}p_{,xx}\right]=0\,.\] | ||
508 | Yhtäpitävästi (jakamalla | ||
509 | \begin_inset Formula $\rho$ | ||
510 | \end_inset | ||
511 | 511 | ||
512 | :lla) | ||
513 | \begin_inset Formula \begin{equation} | ||
514 | \frac{\mu\beta}{\kappa}\phi^{2}p_{,t}-\beta\phi(p_{,x})^{2}+\phi_{,x}p_{,x}-\phi p_{,xx}=0\,.\label{eq:1dFinalForm}\end{equation} | ||
515 | |||
512 | 516 | \end_inset | |
513 | 517 | ||
514 | 518 | Saimme toisen kertaluvun epälineaarisen differentiaaliyhtälön, missä parametri | |
… | … | ||
535 | 535 | Tutki ja esitä vaihtoehtoisia ratkaisutapoja. | |
536 | 536 | ||
537 | 537 | \end_layout | |
538 | |||
539 | \end_inset | ||
540 | |||
541 | |||
542 | \end_layout | ||
543 | |||
544 | \begin_layout Standard | ||
545 | Tutkitaan yhtälöä | ||
546 | \begin_inset CommandInset ref | ||
547 | LatexCommand eqref | ||
548 | reference "eq:1dFinalForm" | ||
549 | |||
550 | \end_inset | ||
551 | |||
552 | . | ||
553 | Etsitään aluksi ratkaisua paineelle aaltorintamamuotoisena | ||
554 | \begin_inset Formula $p(x,t)=f(x+ct)$ | ||
555 | \end_inset | ||
556 | |||
557 | , missä | ||
558 | \begin_inset Formula $c$ | ||
559 | \end_inset | ||
560 | |||
561 | on vakio. | ||
562 | Merkitään muuttujaa | ||
563 | \begin_inset Formula $s=x+ct$ | ||
564 | \end_inset | ||
565 | |||
566 | . | ||
567 | Tällöin | ||
568 | \begin_inset Formula \[ | ||
569 | p_{t}=f'(s)\cdot\frac{\text{d}s}{\text{d}t}=cf'\,,\quad p_{x}=f'\,,\quad p_{xx}=f''\,.\] | ||
570 | |||
571 | \end_inset | ||
572 | |||
573 | Sijoitetaan nämä yhtälööön | ||
574 | \begin_inset CommandInset ref | ||
575 | LatexCommand eqref | ||
576 | reference "eq:1dFinalForm" | ||
577 | |||
578 | \end_inset | ||
579 | |||
580 | : | ||
581 | \begin_inset Formula \[ | ||
582 | \frac{c\mu\beta}{\kappa}\phi^{2}f'-\beta\phi(f')^{2}+\phi_{,x}f'-\phi f''=0\,.\] | ||
583 | |||
584 | \end_inset | ||
585 | |||
586 | Koska yhtälössä esiintyy | ||
587 | \begin_inset Formula $f$ | ||
588 | \end_inset | ||
589 | |||
590 | :n ensimmäistä ja toista derivaattaa, tehdään sijoitus | ||
591 | \begin_inset Formula $h(s)=f'(s)$ | ||
592 | \end_inset | ||
593 | |||
594 | , jolloin saadaan ensimmäisen kertaluvun epälineaarinen differentiaaliyhtälö | ||
595 | |||
596 | \begin_inset Formula $h:$ | ||
597 | \end_inset | ||
598 | |||
599 | lle (joka vastaa painegradienttia) | ||
600 | \begin_inset Formula \begin{equation} | ||
601 | \frac{c\mu\beta}{\kappa}\phi^{2}h-\beta\phi h^{2}+\phi_{,x}h-\phi h'=0\,.\label{eq:eqToAnalyse}\end{equation} | ||
602 | |||
603 | \end_inset | ||
604 | |||
605 | |||
606 | \end_layout | ||
607 | |||
608 | \begin_layout Standard | ||
609 | Tarkastellaan aluksi tilannetta, jossa | ||
610 | \begin_inset Formula $p_{,x}=f'=h$ | ||
611 | \end_inset | ||
612 | |||
613 | on pieni. | ||
614 | Tällöin termi | ||
615 | \begin_inset Formula $h^{2}\approx0$ | ||
616 | \end_inset | ||
617 | |||
618 | , ja analysoitava yhtälö on muotoa | ||
619 | \begin_inset Formula \begin{equation} | ||
620 | \frac{c\mu\beta}{\kappa}\phi^{2}h+\phi_{,x}h-\phi h'=0\,.\label{eq:Analysis1}\end{equation} | ||
621 | |||
622 | \end_inset | ||
623 | |||
624 | Jos lisäksi oletamme, että | ||
625 | \begin_inset Formula $c\mu\beta/\kappa$ | ||
626 | \end_inset | ||
627 | |||
628 | on pieni, saadaan nollannen kertaluvun approksimaatioksi | ||
629 | \begin_inset Formula \[ | ||
630 | \phi_{,x}h-\phi h'=0\,.\] | ||
631 | |||
632 | \end_inset | ||
633 | |||
634 | Tästä | ||
635 | \begin_inset Formula \[ | ||
636 | \frac{\phi_{,x}}{\phi}=\frac{h'}{h}=\alpha\] | ||
637 | |||
638 | \end_inset | ||
639 | |||
640 | missä | ||
641 | \begin_inset Formula $\alpha$ | ||
642 | \end_inset | ||
643 | |||
644 | on jokin mielivaltainen vakio. | ||
645 | Tästä ratkaisuna saadaan | ||
646 | \begin_inset Formula \[ | ||
647 | \phi(x,t)=C_{1}(t)e^{\alpha x}\,,\quad h(s)=C_{2}e^{\alpha s}=C_{2}e^{\alpha(x+ct)}\,.\] | ||
648 | |||
649 | \end_inset | ||
650 | |||
651 | |||
652 | \end_layout | ||
653 | |||
654 | \begin_layout Standard | ||
655 | Tarkastellaan vielä yhtälöä | ||
656 | \begin_inset CommandInset ref | ||
657 | LatexCommand eqref | ||
658 | reference "eq:Analysis1" | ||
659 | |||
660 | \end_inset | ||
661 | |||
662 | ja tilannetta, jossa korroosiota ei tapahdu eli | ||
663 | \begin_inset Formula $\phi$ | ||
664 | \end_inset | ||
665 | |||
666 | on vakio ja siten | ||
667 | \begin_inset Formula $\phi_{,x}=0$ | ||
668 | \end_inset | ||
669 | |||
670 | . | ||
671 | Saadaan | ||
672 | \begin_inset Formula \[ | ||
673 | \frac{c\mu\beta\phi}{\kappa}h-h'=0\,.\] | ||
674 | |||
675 | \end_inset | ||
676 | |||
677 | Merkitään | ||
678 | \begin_inset Formula $a=c\mu\beta\phi/\kappa$ | ||
679 | \end_inset | ||
680 | |||
681 | . | ||
682 | Tällöin ratkaisu on | ||
683 | \begin_inset Formula \[ | ||
684 | h(s)=C_{3}e^{as}=C_{3}e^{a(x+ct)}\,.\] | ||
685 | |||
686 | \end_inset | ||
687 | |||
688 | |||
689 | \end_layout | ||
690 | |||
691 | \begin_layout Standard | ||
692 | Tarkastellaan sitten alkuperäistä yhtälöä | ||
693 | \begin_inset CommandInset ref | ||
694 | LatexCommand eqref | ||
695 | reference "eq:eqToAnalyse" | ||
696 | |||
697 | \end_inset | ||
698 | |||
699 | ilman oletusta | ||
700 | \begin_inset Formula $h$ | ||
701 | \end_inset | ||
702 | |||
703 | on pieni. | ||
704 | Tarkastellaan tilannetta, jossa aallon etenemisnopeus | ||
705 | \begin_inset Formula $c$ | ||
706 | \end_inset | ||
707 | |||
708 | on hyvin pieni ja porositeetin muutos | ||
709 | \begin_inset Formula $\phi_{,x}$ | ||
710 | \end_inset | ||
711 | |||
712 | on hyvin pieni. | ||
713 | Tällöin | ||
714 | \begin_inset CommandInset ref | ||
715 | LatexCommand eqref | ||
716 | reference "eq:eqToAnalyse" | ||
717 | |||
718 | \end_inset | ||
719 | |||
720 | saa muodon | ||
721 | \begin_inset Formula \[ | ||
722 | \beta h^{2}+h'=0\,.\] | ||
723 | |||
724 | \end_inset | ||
725 | |||
726 | Tämän ratkaisu on | ||
727 | \begin_inset Formula \[ | ||
728 | h(s)=\frac{1}{\beta(s+C_{4})}\,.\] | ||
729 | |||
730 | \end_inset | ||
731 | |||
732 | Tästä voidaan ratkaista myös | ||
733 | \begin_inset Formula $f$ | ||
734 | \end_inset | ||
735 | |||
736 | . | ||
737 | Saadaan | ||
738 | \begin_inset Formula \[ | ||
739 | f(s)=\frac{1}{\beta}\ln(s+C_{4})+C_{5}\,.\] | ||
740 | |||
741 | \end_inset | ||
742 | |||
743 | Eli | ||
744 | \begin_inset Formula \[ | ||
745 | p(x,t)=\frac{1}{\beta}\ln(x+ct+C_{4})+C_{5}\,.\] | ||
746 | |||
747 | \end_inset | ||
748 | |||
749 | |||
750 | \end_layout | ||
751 | |||
752 | \begin_layout Standard | ||
753 | Lisätään edelliseen tapaukseen verrattuna oletus, että | ||
754 | \begin_inset Formula $\phi_{,x}$ | ||
755 | \end_inset | ||
756 | |||
757 | on merkittävä. | ||
758 | Tällöin tutkittava yhtälö on | ||
759 | \begin_inset Formula \[ | ||
760 | \phi h'+\beta\phi h^{2}-\phi_{,x}h=0\,.\] | ||
761 | |||
762 | \end_inset | ||
763 | |||
764 | Tämä on funktiokertoiminen Bernoullin yhtälö. | ||
765 | Tehdään siis perinteinen sijoitus | ||
766 | \begin_inset Formula $h=1/w$ | ||
767 | \end_inset | ||
768 | |||
769 | , jolloin | ||
770 | \begin_inset Formula $h'=-w'/w^{2}$ | ||
771 | \end_inset | ||
772 | |||
773 | , ja yhtälö tulee sijoituksen ja | ||
774 | \begin_inset Formula $-w^{2}$ | ||
775 | \end_inset | ||
776 | |||
777 | :lla kertomisen jälkeen muotoon | ||
778 | \begin_inset Formula \[ | ||
779 | \phi w'-\beta\phi+\phi_{,x}w=0\,.\] | ||
780 | |||
781 | \end_inset | ||
782 | |||
783 | Yhtäpitävästi | ||
784 | \begin_inset Formula \[ | ||
785 | w'+\frac{\phi_{,x}}{\phi}w=\beta\,.\] | ||
786 | |||
787 | \end_inset | ||
788 | |||
789 | Tai | ||
790 | \begin_inset Formula \[ | ||
791 | \frac{\phi_{,x}}{\phi}=\frac{\beta-w'}{w}=\gamma\,.\] | ||
538 | 792 | ||
539 | 793 | \end_inset | |
540 | 794 |
Harjoitustyo/JY1_Harjoitustyo.pdf
(1169 / 967)
  | |||
52 | 52 | << /S /GoTo /D [38 0 R /Fit ] >> | |
53 | 53 | endobj | |
54 | 54 | 40 0 obj << | |
55 | /Length 336 | ||
55 | /Length 333 | ||
56 | 56 | /Filter /FlateDecode | |
57 | 57 | >> | |
58 | 58 | stream | |
59 | x]R;k0+4P9=R[AP(v$NC>_\V"%WcZΑCߥ1y֔ޥRтI/.X!41 hYcaGwD p({nӂ#j"9/ExXbIY[X* &;#Lbx'v_h?!=㷴/9)iac9%l.q\;",'_uui2u=!ns | ||
60 | -svaSqڔous\ | ||
61 | j-a!n | ||
59 | x]RMK017UPdۛ!`e4Iޗ+u̼yCUj¨DTr"FJBEza | ||
60 | _Ry[.Dn$r%*fB<bߴ>ɋvO}yxNH#JDGJ80j"C|}Rٔi̎.YbS٤5DhZU' BH"9qmp_sȝrGe 86BZ(M2Uy=B{y}wP솰ne | ||
61 | `A9o]ʩlp=(ۘT>Ĺh%h | ||
62 | MU\?<w~ | ||
62 | 63 | endstream | |
63 | 64 | endobj | |
64 | 65 | 38 0 obj << | |
… | … | ||
105 | 105 | /ProcSet [ /PDF /Text ] | |
106 | 106 | >> endobj | |
107 | 107 | 63 0 obj << | |
108 | /Length 360 | ||
108 | /Length 364 | ||
109 | 109 | /Filter /FlateDecode | |
110 | 110 | >> | |
111 | 111 | stream | |
112 | xTK019$K^~-W^<YYMv&yޗ*fH(&T<# | ||
113 | θؠG|WukTT ǜQ 4^M 8 EvVFxlzeGAL$"6P:B#W>Ɩ݉95X)lq:dCݿ7BUPE9w7yO6cU-Îh˪;w)r$G\:E;bTHDxjo|ƌ4qvoGbzm IrL?=OL ə5Z`X]7gLm | ||
112 | xT=O0+<ڃ}W$:Tb QH j4Aĭ}M*R ,}~|yw]̮Ze6HB<ړbM}ݯ1M\isL@\KA `۬˖iN$:fG(n˦/^-# | ||
113 | nZ'&D | ||
114 | GI Pr30nv)6Gbj0c9Y3ki>lv絭|.PbBxϼ | ||
115 | CPձ?ޕqˬeӻ{)$`EO8Sq_«*V͎)'i4nWߧcH RU8ISM?5@K] | ||
116 | =V*Ag7hp | ||
114 | 117 | endstream | |
115 | 118 | endobj | |
116 | 119 | 62 0 obj << | |
… | … | ||
220 | 220 | /Font << /F31 51 0 R /F14 72 0 R /F11 73 0 R /F15 45 0 R /F10 74 0 R /F8 75 0 R >> | |
221 | 221 | /ProcSet [ /PDF /Text ] | |
222 | 222 | >> endobj | |
223 | 80 0 obj << | ||
224 | /Length 2598 | ||
223 | 81 0 obj << | ||
224 | /Length 2716 | ||
225 | 225 | /Filter /FlateDecode | |
226 | 226 | >> | |
227 | 227 | stream | |
228 | xڽYK6ϯБ`EqʦvG)_>fW~ j0ښ!6F믡o^'+&U%61d4槂oweVb?߿}כ5pX j^Өm-;*8]gaNeqj/0y,}{؊>z7.RTs֝^Q;RŇ1fGf;̝mixYU|Lׇ8qnnsiv,RZ'-qa6c=9ݧqԦE3XnyG:K8y1<YeMkT:ShDŽ{'jMs?VwzdXu\̲+6/VGc `hO(BV5:KyE=^;tjÐ>||G0QBmw9|h0ApC_Ƹ]niA9C`pl+1w `H7L(x]Tҋ7$_|mEŻyaj7BLQaR4lt=~+q,>Yd4a%Tܿܜ;Q!El@7W4, #HBˏ")k_/QuA}di=70SY{9,نBc. T | ||
229 | E#83Nֺvp咽wtA!'S8hl\)JmpC{x[]>f=ɮ$;Aq{R8k | ||
230 | hK@T#@KOGf/ _@}!a5v50EpMAtab[?q/'%a7V#. | ||
231 | {D:'ߡW\:2^b8{u0e|g#n'%v\ 2!̚V)X@"pFސg~xg5 хT\o+R wxCg%69af<l r ̪'Jx | ||
232 | bFG>z":AJJy%>ea63rBے"$(H42$~.7{dSoE,1uwc(3FUL5f,0+VKErCf Reo2$JtU_K8ґZґf0-U2S6LhWb<9~Ik(C)trfp]_݆Vaɗſ%TcdN8-kTC}cRvqvW^egu7g*;y1}ݼl)!y|aFԿʜGvI#7LՆlX"gY AD:cE%5M^y4OKX:1Y(s 0 1 | ||
233 | S,'* | ||
234 | k$=e&Q5ko[4bE"0?ݤLįfFף<{V߹1vKXMvxr+e6$haOUQ<?'n3̌6r/us4ג1_R. LebM<g8!>4 [pR&M5QLT|Xd:g=d7s̮YY?e)-*VĀg%$WvF%Dh | ||
235 | &]!%ͥr^4y"a_1va}Yer+jx^<= oݎ@}@3SYʐCe+^ vL?\7A=NP]aw(cv Tle | ||
236 | ۏazkڳC{*V@$m1ٞ5?ԜT4Er | ||
237 | Bs:?aI @N:; 4J $Z-Rg >WTT`k5Up<N)9H?S?)7 d>?%rϭ |0lA/)c՟ U+ E[}(u<k1DCÁgGx-!~wDJ=vg2,5;|M7KJ$ ;W(oNh M&VMv;W"R&NԺL*KoE͚(V]Χ,U8Q-K+?Pk>CēؠPRaV@Jw̧iOitH{DC_:GOV@H? 41um`p|?xVߎ<7v 5`q[O"Z.)"6l?gz>#25U% | ||
238 | AdfhnT0cWBVK7+KjHL!>OV nNW>|j'oe Ɉxh;Ϛ'n&4H#7XL%R{ӛ#/ | ||
228 | xڭYKs6WQusDIʦv'q%+1#xjM{f[r on|WɍԢҵjce)nn6?z+eY;wd1?{4VqY*)*ܸ6uᦹ{USudjßOXi{aqY8oӄ)i1;vǞv:^3k}:36Nܠ,ߢR>g'5?Pdɇbb<:xn900M|hRuײ$ѱ&$?=eWbi>nqBsrxר*ݹ0^w軹#pjwxV\X1Ь>twHcd{o^K&bc:]XrqC<8a? | ||
229 | x6|dH - 0g7GB:@k)p;p`xl1M`l`(<1y+ [naTFJnt#߮J붩$mӤU:Tq_rp/6a QJUmZ(>`k$|˿QI<& | ||
230 | Y"몮-RH_.*"vr#۳3 V<1;,Zs֍?"{[,RBla?R=KXEx6RߟңTu; 8;Ky, &=>Sx6|RjyϾPa9f]w]7Ip#یg 3`D=LD$|(a{4.ΐGX]-wзNqO gЧ6%aMVpOӊ.D>EIO7t#a vI-)`F{7aN}`Α `0AR | ||
231 | Zaӛ UGzAIZS~Oj5}]W)Ԁu;uf8L6j[rvUP9ɄlPAc13aE5x`R6TM͊ ۯs{A$˪~z | ||
232 | 6D.:%(̥,3[Na6)oK<MU֢MC4rs`|jD^e8f;FVEe:s+$pESh4f \.됵-lE!OrH@(h7~¨el'hP.Qs`q`8a[L\f%*iT,y ܀Z>@RBumیkۺX5\-H x3!{D1a+E8dkU͗IV 2XF"hNG/b | ||
233 | f%@I0O#3NC&{: | ||
234 | TMc1_x4g0 {6܀ u~@W:3u,ANhSE]-0J .OBԫMe}pwߍ;=pNpl?xfIe`%G:#zNA)/\Y5ٞ]'?s?;!)H<°oS&e%o[|{MCe}r(Rn(wCIdH3RvXT[SËl@VĒum^<FʆZN:(8HfN69IT9T`J1Dl -! <rL^T<A.ۺ#khr[>;I)$$*ǎ]7lX[*{q|G~ͱyaXrK) | ||
235 | D/I5/.Ds֨u='PM+0p&B4q\ | ||
236 |