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We obtain the case without recycle for \ h very large (i.e. 10^10). For h small, we reach solvent saturation ( ", Cell[BoxData[ \(TraditionalForm\`X\_1 = 1\)]], ") after a short period of time." }], "Subsubtitle", Background->RGBColor[0.74902, 1, 1]], Cell[BoxData[ \(sol[h_, \[Lambda]_] := NDSolve[{X\_6[t] - \((1 + \[Lambda])\) X\_5[t] + \[Lambda]\ X\_4[t] \[Equal] D[X\_5[t], {t, 1}], X\_5[t] - \((1 + \[Lambda])\) X\_4[t] + \[Lambda]\ X\_3[t] \[Equal] D[X\_4[t], {t, 1}], \[IndentingNewLine]X\_4[ t] - \((1 + \[Lambda])\) X\_3[t] + \[Lambda]\ X\_2[t] \[Equal] D[X\_3[t], {t, 1}], X\_3[t] - \((1 + \[Lambda])\) X\_2[t] + \[Lambda]\ X\_1[t] \[Equal] D[X\_2[t], {t, 1}], X\_2[t] - \((1 + \[Lambda])\) X\_1[t] + \[Lambda]\ X\_0[t] \[Equal] D[X\_1[t], {t, 1}], \[IndentingNewLine]h\ D[ X\_6[t], {t, 1}] \[Equal] \((X\_1[t] - X\_6[t])\), X\_1[0] \[Equal] 0, X\_2[0] \[Equal] 0, X\_3[0] \[Equal] 0, X\_4[0] \[Equal] 0, X\_5[0] \[Equal] 0, X\_6[0] \[Equal] 0}, {X\_1[t], X\_2[t], X\_3[t], X\_4[t], X\_5[t], X\_6[t]}, {t, 0, 150}]\)], "Input"], Cell[BoxData[ \(\(plt1 = 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.20255 .30881 L .20952 .30887 L .2166 .3089 L .22331 .30893 L .22995 .30895 L .23609 .30897 L .24231 .30898 L .24917 .30899 L .25562 .309 L .26258 .309 L .26926 .309 L .27629 .30901 L .28287 .30901 L .28899 .30901 L .29581 .30901 L .30201 .30901 L .3084 .30901 L .31533 .30902 L .32196 .30902 L .32897 .30902 L .33533 .30902 L .34127 .30902 L s 1 0 0 r .02381 0 m .0242 0 L .02456 0 L .02497 2e-005 L .02536 6e-005 L .02572 .00013 L .02605 .00023 L .02642 .00039 L .0268 .00062 L .02719 .00093 L .02761 .00135 L .02836 .00237 L .02926 .00403 L .03008 .00598 L .0317 .01096 L .03347 .01783 L .03669 .0329 L .04349 .06786 L .05073 .10136 L .05724 .1256 L .06428 .14594 L .07142 .16145 L .07814 .17243 L .08479 .18063 L .09181 .18713 L .09836 .19169 L .10447 .19494 L .11125 .1977 L .11744 .19961 L .1238 .20112 L .13072 .20236 L .13731 .20324 L .14431 .20395 L .1508 .20445 L .1569 .2048 L .16362 .2051 L .16979 .20531 L .1761 .20547 L .183 .20561 L .18954 .20571 L .19652 .20578 L .20364 .20584 L .21035 .20588 L .21702 .20592 L .22317 .20594 L .22943 .20595 L .23631 .20597 L .24279 .20598 L .24976 .20599 L .25681 .20599 L Mistroke .26351 .206 L .27013 .206 L .27626 .206 L .28312 .20601 L .28932 .20601 L .29575 .20601 L .3027 .20601 L .30936 .20601 L .31638 .20601 L .32294 .20601 L .32906 .20601 L .33545 .20601 L .34127 .20601 L Mfstroke .286 1 0 r .02381 0 m .0242 0 L .02456 0 L .02497 0 L .02536 0 L .02572 1e-005 L .02605 2e-005 L .02642 3e-005 L .0268 6e-005 L .02719 9e-005 L .02761 .00015 L .028 .00023 L .02836 .00032 L .02878 .00045 L .02924 .00062 L .03008 .00106 L .03095 .00167 L .03174 .00239 L .03351 .00452 L .03514 .00712 L .03669 .01004 L .05073 .0435 L .05686 .0562 L .06358 .06742 L .07023 .07601 L .07725 .08289 L .08375 .0877 L .09073 .0916 L .09781 .09454 L .10451 .09663 L .11115 .09819 L .11729 .09929 L .12351 .10015 L .13038 .10086 L .13683 .10137 L .14378 .10179 L .15046 .10209 L .15749 .10232 L .16407 .10249 L .1702 .10261 L .17701 .10271 L .18321 .10278 L .18961 .10283 L .19654 .10287 L .20316 .10291 L .21018 .10293 L .2167 .10295 L .22281 .10296 L .22957 .10297 L .23575 .10298 L Mistroke .24209 .10299 L .249 .10299 L .25557 .10299 L .26257 .103 L .26972 .103 L .27645 .103 L .28315 .103 L .28931 .103 L .2956 .103 L .30249 .103 L .30901 .103 L .31598 .103 L .32308 .10301 L .32979 .10301 L .33576 .10301 L .34127 .10301 L Mfstroke 1 .857 0 r .34127 .51503 m .34166 .51503 L .34202 .51503 L .34243 .51503 L .34282 .51503 L .34318 .51503 L .34351 .51503 L .34388 .51503 L .34426 .51503 L .34465 .51504 L .34507 .51504 L .34546 .51505 L .34582 .51506 L .34624 .51508 L .3467 .51511 L .34714 .51515 L .34754 .51519 L .34795 .51525 L .3484 .51532 L .34922 .51549 L .35001 .51571 L .35074 .51597 L .3524 .51678 L .35415 .51796 L .35582 .51941 L .35761 .52129 L .36084 .52539 L .36819 .53659 L .38198 .55732 L .38888 .56579 L .39526 .57235 L .40804 .58227 L .41426 .58584 L .42113 .58902 L .42812 .5916 L .43453 .59348 L .44742 .59621 L .45373 .59716 L .46063 .59798 L .46717 .5986 L .47415 .59911 L .48127 .59952 L .48799 .59982 L .49466 .60005 L .50081 .60022 L .50759 .60036 L .51394 .60047 L .52042 .60056 L .52657 .60062 L .53333 .60068 L Mistroke .53951 .60072 L .54613 .60075 L .55226 .60077 L .55911 .6008 L .56532 .60081 L .57175 .60082 L .57869 .60083 L .58535 .60084 L .59238 .60085 L .59894 .60085 L .60505 .60085 L .61185 .60086 L .61804 .60086 L .62442 .60086 L .63134 .60086 L .63794 .60086 L .64495 .60086 L .65145 .60086 L .65755 .60086 L .65873 .60086 L Mfstroke 0 1 .571 r .34127 .41202 m .34166 .41202 L .34202 .41202 L .34243 .41202 L .34282 .41203 L .34318 .41203 L .34351 .41204 L .34388 .41205 L .34426 .41208 L .34465 .41212 L .34507 .41218 L .34546 .41225 L .34582 .41234 L .34624 .41247 L .3467 .41266 L .34754 .4131 L .34841 .41374 L .3492 .41449 L .35097 .41675 L .3526 .41957 L .35415 .42282 L .3609 .44166 L .36819 .46529 L .38186 .50477 L .38867 .52023 L .39502 .5322 L .40768 .55012 L .41446 .55712 L .42065 .56228 L .42755 .5669 L .43393 .57031 L .44671 .57524 L .45293 .57695 L .4598 .57844 L .46625 .57955 L .4732 .58049 L .47988 .58119 L .48691 .58177 L .49349 .58219 L .49961 .5825 L .50586 .58275 L .51263 .58297 L .51974 .58314 L .52646 .58327 L .53309 .58336 L .5401 .58344 L .54663 .5835 L .55273 .58354 L .55949 .58358 L .56567 .5836 L Mistroke .57201 .58362 L .57893 .58364 L .5855 .58365 L .59249 .58366 L .59964 .58367 L .60637 .58368 L .61308 .58368 L .61924 .58369 L .62552 .58369 L .63242 .58369 L .63893 .58369 L .64591 .58369 L .6525 .5837 L .65873 .5837 L Mfstroke .286 0 1 r .34127 .30902 m .34166 .30902 L .34202 .30902 L .34243 .30904 L .34282 .30908 L .34318 .30915 L .34351 .30925 L .34388 .30941 L .34426 .30964 L .34465 .30995 L .34507 .31037 L .34582 .31138 L .34672 .31305 L .34754 .315 L .34916 .31999 L .35093 .32689 L .35415 .34209 L .36819 .41443 L .3753 .44483 L .38174 .46777 L .39478 .50264 L .4012 .5152 L .40814 .52615 L .41466 .53437 L .42181 .54154 L .43497 .55092 L .44147 .55419 L .44845 .55695 L .45553 .55914 L .46223 .56076 L .46831 .56192 L .47501 .56294 L .4816 .56372 L .4886 .56437 L .49505 .56483 L .502 .56523 L .50868 .56552 L .51572 .56576 L .5223 .56593 L .52842 .56605 L .53524 .56616 L .54144 .56624 L .54783 .5663 L .55476 .56636 L .56139 .5664 L .5684 .56643 L .57493 .56645 L .58103 .56647 L .58779 .56648 L .59397 .56649 L Mistroke .60031 .5665 L .60723 .56651 L .6138 .56651 L .62079 .56652 L .62794 .56652 L .63467 .56652 L .64138 .56653 L .64754 .56653 L .65873 .56653 L Mfstroke 1 0 0 r .34127 .20601 m .35415 .29359 L .36085 .34738 L .36819 .39318 L .37502 .42608 L .38138 .4504 L .39438 .48636 L .40148 .50026 L .4082 .51065 L .421 .52488 L .42761 .53009 L .43462 .53443 L .44724 .53996 L .45371 .54196 L .46066 .54365 L .46771 .54497 L .47441 .54595 L .48101 .5467 L .48714 .54725 L .4934 .5477 L .50018 .54807 L .50732 .54838 L .51404 .5486 L .52069 .54877 L .52771 .54891 L .53425 .54901 L .54037 .54909 L .54715 .54915 L .55334 .5492 L .5597 .54923 L .56662 .54926 L .57321 .54929 L .58021 .5493 L .5867 .54932 L .59279 .54933 L .59952 .54934 L .60569 .54934 L .612 .54935 L .6189 .54935 L .62544 .54935 L .63242 .54936 L .63953 .54936 L .64625 .54936 L .65274 .54936 L .65873 .54936 L s .286 1 0 r .34127 .10301 m .34754 .2052 L .35073 .25759 L .35415 .30151 L .35762 .33632 L .36085 .36236 L .36819 .40642 L .3753 .43645 L .38201 .45766 L .38867 .47389 L .39481 .48569 L .40159 .49595 L .40793 .50352 L .4144 .50963 L .42054 .51424 L .42729 .51824 L .43347 .52112 L .44014 .52358 L .4462 .52534 L .45275 .52685 L .45975 .5281 L .46616 .52899 L .4731 .52973 L .47975 .53029 L .48677 .53074 L .49331 .53106 L .49943 .5313 L .50621 .53151 L .5124 .53165 L .51876 .53177 L .52568 .53187 L .53227 .53195 L .53927 .53201 L .54576 .53205 L .55185 .53208 L .55858 .53211 L .56475 .53213 L .57106 .53214 L .57796 .53215 L .5845 .53216 L .59148 .53217 L .59859 .53218 L .60531 .53218 L .61198 .53219 L .61813 .53219 L .62439 .53219 L .63127 .53219 L .63775 .53219 L .64471 .53219 L .65177 .53219 L Mistroke .65847 .53219 L .65873 .53219 L Mfstroke 1 .857 0 r .65873 .60086 m .66172 .60087 L .665 .60087 L .66585 .60087 L .66665 .60087 L .6671 .60087 L .66758 .60087 L .66798 .60087 L .66842 .60087 L .66923 .60087 L .66967 .60087 L .67008 .60087 L .67082 .60087 L .67123 .60087 L .67161 .60087 L .67247 .60087 L .67296 .60087 L .67339 .60087 L .67425 .60087 L .67505 .60087 L .67599 .60088 L .67686 .60088 L .67781 .60089 L .67881 .60089 L .6805 .60091 L .68207 .60094 L .6838 .60098 L .68565 .60103 L .68742 .6011 L .68904 .60118 L .69273 .60141 L .69599 .60168 L .69944 .60203 L .71202 .6038 L .72543 .60609 L .73832 .60823 L .75203 .61016 L .76524 .61162 L .77795 .61267 L .78503 .61313 L .79147 .61349 L .80448 .61403 L .81088 .61424 L .81781 .61442 L .8243 .61456 L .83145 .61469 L .84458 .61486 L .85106 .61492 L .85803 .61497 L .86461 .61501 L Mistroke .87179 .61505 L .88504 .61509 L .89161 .61511 L .89861 .61512 L .90528 .61513 L .91248 .61514 L .91886 .61515 L .92586 .61515 L .93252 .61516 L .93954 .61516 L .94606 .61516 L .95304 .61517 L .96013 .61517 L .96684 .61517 L .97619 .61517 L Mfstroke 0 1 .571 r .65873 .5837 m .66172 .5837 L .66344 .5837 L .665 .5837 L .66541 .5837 L .66585 .5837 L .66623 .5837 L .66665 .5837 L .6671 .5837 L .66757 .5837 L .66801 .5837 L .66842 .5837 L .66883 .5837 L .66922 .5837 L .66996 .5837 L .67037 .5837 L .67075 .5837 L .67161 .5837 L .67207 .58371 L .67249 .58371 L .67344 .58371 L .67429 .58372 L .67517 .58373 L .67597 .58374 L .67672 .58376 L .67841 .5838 L .67935 .58383 L .68024 .58387 L .6819 .58396 L .6837 .58408 L .68565 .58425 L .68879 .58462 L .69225 .58516 L .69925 .58669 L .71265 .59081 L .72554 .59529 L .73926 .59969 L .75247 .60318 L .76517 .6058 L .77869 .60786 L .7917 .60928 L .79882 .60986 L .80554 .61032 L .81836 .61098 L .82498 .61123 L .832 .61145 L .84463 .61174 L .85111 .61185 L .85807 .61195 L .86466 .61202 L Mistroke .87183 .61208 L .88509 .61217 L .89166 .6122 L .89865 .61222 L .90532 .61224 L .91253 .61226 L .91891 .61227 L .9259 .61228 L .93256 .61228 L .93959 .61229 L .9461 .61229 L .95308 .6123 L .96017 .6123 L .96689 .6123 L .97619 .61231 L Mfstroke .286 0 1 r .65873 .56653 m .66028 .56653 L .66172 .56653 L .66254 .56653 L .66331 .56653 L .66373 .56653 L .66419 .56653 L .66461 .56653 L .665 .56653 L .66538 .56653 L .66579 .56653 L .66617 .56653 L .66653 .56653 L .66694 .56653 L .66739 .56653 L .66781 .56653 L .66821 .56653 L .66865 .56654 L .66907 .56654 L .66985 .56654 L .67029 .56655 L .6707 .56655 L .67161 .56657 L .67242 .56658 L .67329 .56661 L .67411 .56663 L .67486 .56666 L .67574 .56671 L .6767 .56677 L .67844 .56691 L .68026 .56711 L .68219 .5674 L .68565 .56809 L .68878 .56893 L .69214 .57004 L .69824 .57254 L .71195 .57952 L .72516 .58644 L .73786 .5923 L .75138 .5973 L .7644 .60093 L .77103 .6024 L .77823 .60373 L .79156 .60562 L .79818 .60632 L .8052 .60694 L .81783 .60777 L .82431 .60809 L .83127 .60836 L .83785 .60858 L 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