From 61d9ca8a25d3226be8effb0d22ba99b238040293 Mon Sep 17 00:00:00 2001 From: Cory Date: Tue, 24 Oct 2023 22:23:50 +0200 Subject: [PATCH] Fix mistake --- latex/main.pdf | Bin 753605 -> 753602 bytes latex/sections/results.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/latex/main.pdf b/latex/main.pdf index 2be3529dddf6d80235ff929ed5a972a2f15ce753..5c4a2a88bf80a9158988e6f3537ef201c4501bf5 100644 GIT binary patch delta 7446 zcmai$Wm6msuZDpI78ZARD^}cHi+gc*hf>@YcZVXyp-6Fe>EgB&cU`2o7J1OO=NFur zT$$WSCZ95y48OAvyt9Wyz_%bw`oIgO&nPj27xi6|_jz&O#QSL<*y(0RlD030fESTs zDJg`+o53M66Q11x1Kv!k!cfi^|0-iO;c@G13m+-z+DwXWOTBM}{#E1!=iCLoT~B|Y zi=%}EEVom+1J(lTDo&FTDLISZg#a?SXX_ir@9&54tOceg>+c)Js7F^S)`pPyIEOuO z)7|dLC~J9bq|FzPg+%RFR)?Lv-&h}?eZJliygdCRU~4C>C2Gy!{#sO~sj0l8&cc|% zh$Qj+LeOnWpu3N0$YAsK)aCBC>b>YsWnbD*r3({b08 zU!}uel*Gwg?ZwZkiQ;g4e-$uxC4nxI;N!~S--^~H%&eeQw7`hdoR_|n3;TYndYYc> z+K5{fLoABv44l7epG)OU>?ipgaiH4&K~1O$+#U`{k+xu^Qv#~oM;dKz>by&LO%<5! z)jmXfFXqPNj%|PCi})@}3$wBq86##?(4H}~ui~?bYujT`>q#CwK&V;I;3J+_ z6kJzS+>cTNIP@F%xUPq-HVXD`&v@@P@VId#)gviamLU;FA&77c6c96V94-A3B&|sJ zq**bxAMT70%Oi1kGzishiJ2##;T@M?RBf5FsB0`4kmSK7kfVUSm1sE#H z(1**8e7spzsH_o)*Fdtz*uQH!kIQn_3swHXN?V!xH5$t!$?#WillXhE6bDC+=E=kH zT?E<21{$kPra)1E3s_L!{@Fi891(|yj zn`dymM)0q`DfK@_MWX5N?(7~RU1JvMq)#GwxQ!K0A~E?-Zk$vCeq+Kvf}I!IAmesInf!aj}&w|(+`#k~-0 z!dg%Aw{a98AZDRy3Lt~+?{?Ii2l%pEmNk^l<84VM@`bqO$}%1h-wuj4M00%vhcl76 z`{mY8e%~;?3KOF4kEN&x$pjT_%W-#C0Gp_UlkrC&sRP%3R1>QH;Ce+mC^NL!hyHxK1NCmOg44I->Jg3G*W*C9-s2n|gdFPcWGoX{S`?_t4k+jm-uRni$b|sm8nwntK?BS-u`9P zm9nr&rdVB50;9cQkj;WD?vk;bB$ym*laU&2(HB0X18ZEFO!ex zGN|aK7fYw-A=FS<11Te7m2e%q(>4*cZV*BIFzkbdc7SN%g(any7{kac&Nv;!qEA;^ zgHj=Es6EMmsT?!$A--=v-5pq#hIOE=yO4&OJJB6F!pAE?^`J^dr3D(9tq_!S#|+f! zkw6W(K~C@mMB@g91vex8e4-g(MBu z-Gc5&x$l`z2NsP3ibBDVXf3X~%^vzxI%j6M!d!D@Fx$V4tGKeV4+WBe~mf4flB6Cd0CNQx?;us`q6Oc2;ZQN=> zP#Vp%2j9|Ljh2Gx=OlT$2S>Gbi9&$lrMm-pS6Q;cAB8`h?JjeO*DZYwn9x1w{Nayl z*zO(pGq-M6O6QRw-Bd;oTPNJ8j9=A`I5sf#UOElvJ(xCE{bE*pu4F0iTW`A2T0g%t z$3HGAD7n>E8L+L47)WDAo?wI70{CwvTIxK~BsTQZH(%ftpZ`uREHiYq4JKiAFE zIQanAo_;jGZxav9H4Rur3SO@}et}hE^}Frh3nbr20l7Da1U_)5tz_YZOU{&zC>LVo zJ)2@kL-w|{{p(~!n86szq0Y4wNNQ)w4owPr7Y&8G5qb+|0jywU!Rwfz_;;1b7+t8V zf=dT}EAmW(6C8Jn*;8vtA*AC%TX%oX0%^{7OIpp5FV4#XlOoU2^gA@XM+T6FHt@h~ zHJ#65Y%0NNnTkT)H~p~|Oo=3N*}UH57Q`w{X^Pe^oF4}nn_Bv0347#Ikq~r1+8jtD zrPLUAjNdM=M?mac?p+2h04^!z@ut?X-3CfDrB!b!9esA#4`Ewt z`KzhmkzaUfMaI9_#p<@V8;bsg`F`xbMx*=uj$vAtxnpJSHMN9bSon4Qv?MqS@(jX@ z?gt~Z_k#gRr|{fa5Pd{;a2rAJwi%?I(IuMtB7|u^XN9cWA$=rqlfQNp%Q%*mIa4;W z#JQrsZyT7lR_$}p>Objj+u3oov$M0|8`6w+?xJhG)~({0JZCq-nnA;Zv?gV@)L>%G z-;j}`&Gz|_d_u#T(p|ortqV4kO`9IsnggL`E|nREYhJ1}2LVLEBM~aXnA}|Hl$VL@ z+-2nQ2C>JX^ZGlw4uY{M$l2FxlQEPj`}p!CGnN$5r&H@;1i5~nBu{xRrRp2GZc|J1 zrlc)Gv2}nXQpxiMS3~Idn#=<$Z2p)&#*qjijYXf8fUf2>I+1o%dO8Xv)XOC{81CgU zMewW{@(!`2`fwxQ2)sQmg!p|BnCsDv?yLp1{#Twn`8*QF0g~*g!buOvMv<2V*w`O(GS; zEBrWYk^CXqEW)LMj5Pj*Z2_@lP=6E@r5V9(&f*RvP(cDOF_Unm(}mf`f-ZHW5OGk1 zQ$I~?;it$9WlTu-Aj2Ta?qjmpKc(S!|M`;Qtww~ZUk+u8{44RG6^ysg+q8|wnlHAn zW$cYu+ThwE1CW&l00Wt&yrsOU#1nVVfF=J}2f2oIk@F{e%y>9g#*ev~oP?g)*`Ih- z!n*LanBboXtp`IIs5w#v6AFe3=13^NoEI8otB{=VxeZWPHKjzIGSLoEw2#s``UG(} zz*{;wj~=~s>v-3eK1=2I0`Ygbc-I}S<)3e>LfDDwhcAbhVdJbhq)f19$2r^jqRY+^ z=d~fx8QLCbql(`Cw4Y>9PSCX+qp3B_;I(Ob2<&iga5rD)Omru#*Ev^c*Z;hU8k{7l zFw+SHHZJ7#!Eqy_;@)3)WWUt@$m6i>E}tk9r6gGkL1&S+xIqb8BDAJAY4@ACSL0s5 z=`7}C_tbLC&>$=gQu~9#FqYq$OQsj$5yyZ8dlSc#czLBF$+t}Dj5et8nLIef8pxS4 z1g9JMHazdp>swiv_zXbo_9N-FfPSm2zjA!FI8G0T%ky*^8h8)=R@*)|N9~p!>Rqne zajZ4fHevpW^);+t9}268qaVV&U>0ZA`dJKL4O#Dl=UlV`gHV4o!%N3saSe_8_j26W=w3`ckW zs2~zZD<(bwUmX95*AmC!Dm_=HpqP<&)6&FK9Q^}^4D)7C9|@sD%wSju@5e|Y;of$1 zBL?NwR-8ut2xPV0Mw1Vd)YAjk$iZju)rwg8CYt!m;Gg)E&-kFgDKJmM?dwW$%av4& z@pS}x@dtZ2bZKF`qaG6&u$CNC7;VNgT9VaLwfN{i+ap{-%1i7NLqz?Ts8p=kY*$s{ zL2-(Kw@&@kRDH1`^gT0Qnd&%vU@o?Hj8dJWhw;Q;%uu2dTaB^C?8IFhx_}d=aPuJz z;?g-0EL5iHQOt_N5pXEJqk#JXA3^aiY4{TyG(nW@@Vt=Yp3|t?Q+ux3Pl$@425s{N zfL*i*2d$kd?T9+5I4|MEW@Cis>n%&WUzJb~Al$Ce{eMXg^rKt@5!h^qcyTG_eAyQ} zDzrNvCD4~1=?Q~|coJkd3)f^~RpBDk03jNXOvy4m>vXjVb+9RCd3#YLvdmyi1HC$7 zy4|?_m_%;Iw*SD&j~5)@m}E1bX#NMML7tjX1=3ixDs%kO^^`Up2Vm%zeJ1IBYfr*J zOLB@D<%!Juugs3e_f{LW3|7`H>cW<1zL#J&_FD2#v$k-e?AQO((*xw(+Um!Zc zxQbMjI{(HL?+1EbMD00S>hG7gkM7L}FW5LlPb4F_(+B!mgCR+MyDA%aL7f{M5pUl& zPA0|lI!h@!&bs_9@fl|O?fO$+Oox&Tf~aCGa<(4QQX;jpgl?a-e7T3vSIpR^f3psC zCnT5=zzjMKzrk7z+sb@}>aU)2J-qnYhq2JE18GdzY<*v|px%u&%dr2*^VcIET|YyW zz65`qCV~aVfH*5hAl-hQ2}d<&_KmT;xi*yWl1^Jy?awrY`Y3o9(S`jZbxR z)#^uErxdun#1)+tgc>8wI*oONAb}FVHs^(z?w_Dq@TqJ{)bhH3W%Gv1@DIj-LkYLT z#qVQ;cRHRKFU^jQn)R%+ebsUzZdFQoR)g@F=0WSj0gc1b%Oxi$MsV(0>Cx+stw)ZV zxaD^uI^eZ$$|<@ooeT;lGBO#pk6NOH>O(&tl|%`C&$T^Z!IEKQ*R_x7k7}YsV8ZQq zB3RiYIR3HvG51mG#pDH$aF|r8I!V@%LHZi++L|uMvsycywHN@Z&7-$vxI#3F5 z4sDIi$&QbF)a=1gZp3xcj8A-2NeuD0oP zlIzx2W92fDd~b_CH_aC9!#8rZq$*EZzirC`&pg%0+)5M`4YJg`=zWqQ$N0iKWL8O& zISD0CgJl~GaI5N9Vd_hNULBZc>_I~@>|qwj)ne;r))mQ4^6kgYjkG`HTgXapJy1J) zLKVn%4+E-dRwxFXQK-eHrped{=z4_U+srRqRw}q)fU^D&QP_C}%%B0$T}NhDaiEZJ(xM4$Q3ON`ZuF|oM+-ZF>|bvgTB7>{|I@{>(9 zIZapDynbAqXeK4?J)8EWw4M_R_!JWg`8`*!y-_$#+EM z;?=S^tNZ@j`7SGi^UKLDDxOnPHYM>KHI`!b-_8U&981aq&c@yBh?Qt26=N<&m63?? zY)%q9Mymm9mFxu6bS?|-f61?F*LmLmbd(?|%s%E{O*Dc6%VIQQ+`hWBmLaL_2~91# z5;lg4=SEe)`QLt(hQbuQ!4pBQGHS57AXiA>LXhjGN!Zolv8~$NK!8xU)_vK@ zWYW#@XlHy1SdZ#P#mFiD7FoSar(oJP5gM-bV1nx)exN%PcH;4cwWLkx@`sn^VJMRy za+ketkKsPcmfE=WtnPmvjZyQ?CyR8S6&~!lvxeycWV>o6&HA!XVodt&l=V)}W3+>Y#*G}-EU6>z!KZtsHmG;8JxjV#8#mJig`X$~ zj%fw9wkpK*n2WVR_ng1|NHF{2qt~-FkGpBgSZ>1XrCPDBUCmX+bbyviG;nloG*L~z zC^i5!9u>bB$Zlw(z`5RV?dzogPL5|C(;wA9i76+avTo?QX_p8dhM-5k&qU9T zUpBB0Y#Q|{N?qY&isjY9wc*|}E4DB@vIY5P@|#)r*_gVpXEHzjIx97Jg^HW8$%xvB z@(nlI(Vj@Xfl_G?%#+{v{ZcX5In_FhSyUa^9qhj|KL-zq_^J*);bdJATAK2>qGcOQ zqzs1T^@O7Y1kz@JI@5?`Kb(7%VljqAQM`gJC{MZb*l5W^o*SGx5o(O<{6zR)@;nb+ z&0P=(53vSSGI`q1(Xu{8koW+wuIcr4vVDmgFg2dcF#%CZhY(5>HngKA&v%k-zoPD* z6a4x|2y5zzMLThTsiCVIS~7><;xqa2a6KDd?&^Q#Ir%pA_r?&+({oF$p!c)u(=+hL z(aGHVdLdJzN}#am+qV%Wp%tg=oVZR{?E_}nJ{7v;!JOI1uaUpegUzcY`Ipm_e2e9M zw(}}6RF?C4JJebc(Kq3lJ_JAEO9wEJ`cR`&(qr8_n5Zrx%s3E{DC!vX|CVul5S)@b z*jENC<#eV|MCUVUa(kl_LRKcYbCN$$Gd%??5qan#nocJ}qs7n(F@ND7a_S57emzFHaV;I~w)>1??*C zXgMfaa)P|FJluj@0pf^u9!GF*HDvi!0#GQ5J)@^UiL;?$!5Z;J_tL&e6`&eNWn zi%*CzeOBoMm?2Zq`P*mw(aWHq`a#we>EbDwW6}9J_z&!5o`-}JD#ZY#Fe_}ugc3$X zB1|%GWID8xC=^CLq7L)jxoV@m2Hr0}!|2TyB0C|^&&~fGY~1!;20!H8O8gPGni^&z zv3j*|MlJg-H?~Nn zz&I-;WtRrhLfDMc)1%=(DWpshC?-B!tj=#J9p7{!(;D$V009 zNC|jeHRm9<^&@pcbfQ#9FV$Cy)mgSt9d-Z*wXc7Vs<1qV?~U*xWeekZWQ2(C{KB7M z!U}P4$0kRJhTs%kQUXRHsGI<`Fl}=}oT|*dCEl$$uESrV`fwmyoFg_nzd`J&FCiQ= zMl^#Sgjep=6OwL7!YnhIq0&e!#2;KV9;l;=3JjEbo*{}(+f;{aQmSEU00hhrBGlmj zB*_rJ(^J1m8X?hB*$;6dR(`4k*et1R%?Eo*uKc1Iw>AeME>QA^vjm$b426dbMLDu@ zQ__0|Usd&a6pckgP>7KfwX#fSmPa5Fe9M>)iX;FV^rsGf2Gi&ZfEU``5?jIiATR}V z%c8L+=>TBIpY@eIFHU8+!8C%0;)4l$!3BihvBb*vS5m%5J@1S zFm)v$B~WlscaHwfi$Ri#1vvph4>4x!->OK6+&K~MOVWH`Fr`S`J98E}f?TPFiV9%VG9?6~pji68{VQsp4>``ORa^IX*Do;K6Ak+n@A{I?c zo<4Jq7y#eoE(2#ESYAs8*A1aw0gS-OEGCARnj_3)x#DvAY>K<12y!AVsEkc1+WxJw zQW7G_fSl{>ll=1aQt=#Z@j?$8ee_81AKmdr<9~)3M#fEv#@(5K`MY0Kt(wXD7qG;N zh6sn+Th5A{#^ZkjHs?PKXiFs%_gs913ZI3h)q5&eZ5&OUS}wW7>4@h4@!~3FtUv7_Il?V3Dlqh)IQm&s z;ad>)WSV>aqAYa^KBPbTphyER@%>^g`pJzyv!>rhQ$v0Hr2(4sR_?=GD^cKTJ4ly` zd^_rVKctOwQYR*>#^-|Oa=c*Iq+$6(hK@`&jbhR7hhW;Kf+bySB0YaqyMi;TuJnzmL-HoX^!#Zn3Tt#q30<6(Dm87ZU;!ns7Si0_U^CrX=vI)L zZay^F%G&hPVw%Al72;T71l=6o?r zHA2{TV>Pg+eB;tAci`33<*fNY)YRoN8<uAsnX=+Nv{Z>bWx{id^&4Sn}e zTk3$mKYU%=QPh%hIIM^m_>HF&tg3IAqj7=z@0F?S$!a*X7>F8(P^CjPx@TITRJPAn zw-+y*@un%>OON=tbrh5`qxX%|o!6q0*@B)?kE?9UMRvPiAo}tHcxTu``17fZe z!Hn6xqXyuwTQBB9IPwh2cS#<5_}U_jmhf6h?IJv9fJxDMW?vvr{?45b^c`9CIwLC& Qj7EdP1!7>3Q#|1HJ;Er5gpv;xa_0yj95(Ml+P)mclEKAspynEGQj+wD>i4nQ6+TRH?%&oX_U>^>9b)9g~JIFk1=d znJPR~IMY_pn7ToYhN>&qs72VG&TsB2Qt@_QuCc>={8ag-jT<_Y-TR(oL+aZPxLmV) z+?*db7ewurMpQKCT~Le9^+_tT3os#sVMY|6fC;~diOGD6nDB;iujY_&xeqpfGfyDl zmLTCGBpgA)%^~5=thNjZNebx$2tKCCk-d66It7b$c4{L!F}*aIXuW|9wF(ub9>PU(@Ru zGq`grth8NTG#JDD*Nw4?$Gq?WPdh(X>3C01)mgL-H5g?$#L9%~x+(X6`-f{-28^tv z$!`(L4_H@uf4T+Av-!Jgkpt944vREU-(j;RW(fTr`k^{deQ2pH<7a)SR-1}~W7TZ% zbO4vqPLf7~X%j8*3mm*^zd?@+4K(yVoC)Q9T+O?@tB$~0bkK0BAgmkOIy2#{cVK~7 z{o&13_H&p)s+oC+P;r@mdz`4EW%}W?fh|6qExH9Lu0}$eC`|OHxeI3<%OebbJnksj zSKEPVWh^%}Y*fL?PJ0NAhvUA6~1Cklt}eN}FM;04(jZD_~L+oNR3rAEr>|&YZ7%Q3f zntJ`TU{gF}P@DAnDAGVVA2PBz9n!jqRmP33lqy2-z><6e zl@1J3Ef@hZoPvvgPqKmHGvX*9cb;^T3x@K*MLwi#|WZqRe-;HwpdnyYt|Ux229{XEC?MMDvziBF2o_7C^1MUB##7#@mdQ( zaUgaizICi{Vs6lIzep*cf;%XseAqumMWdJ~VtO~yxPju=ZM_2&2$n}&4oNUjt7+r;h1dofS zY0d6LiTpna9dI=hav@2)CkuR%mC_^5CV0*?EawOpJF}X{_C-UyX;^F44Y&0Ci=NaRM7GPX_QGpB2 z{atvn0b#ld;0S;N2`4sJ;qs0aoj$1ung6+eU(#Z{S-_>9GHh)qfdj#XqyQtt`OPJa zzkhrhm>&@#nHTook@z|1KA!klAueJ3%ku>FKaeNrnE0W;dh%Df?^}`tum&!91Z*V# zf~oW5FC1dc#Uzj5GUf|h%<>2x(+6lDFIP(*E+jZby_|U+Q^1vH%Vl86=QaR4 z7J$An2gFbxkchRgbNmm3c8(&-39;8k0Rl;SUx+DyrWD|rr;NB+C(>r2R!0d@HP%ke zv8y)qdMIy$-yFy10+HXPXQGCL$pubC54y8IG0xV1y76b;h<^vR=Y5yK0t*v|#D4;} z#D4>h>j5^C(Ml?RTXWk+mVVc-z}qCdQ)u+P+m)KC*owWGNjBctvy&N@A0QGU8IuG9 zg0?fie!s5)P?Tg#w9L6|3RQyog43r@pBqm1k=xqatjM%?nbaPo&y-gvLuLxJgU+ns z`y#V}rOcdSsWRtKqR$sLGuma*hBE_LSy-JJqcSO@LB#-nvzDk}3gdv+giJaPGBJ}L zfW{V?QVyf6#Ppoof(Dg_lL)DR83VlZ=mAMiVUz(ar~z1K-WIIb%sWFoJ_DKpm6-X+ zQBG!|ut10bK}OJn`GO~AXR@diVQdyXhdZu9VTiGyRZ8bj1No}(?Bj|GNfhK-w5$Qn z6cIFlQ_?7Z6;T5Vz!-OCJVs!VzzlAK3E+|;$F1ZX;JLI8ZR5!qnXqWoyd<0ilbpor z9oQ8txNjUrL{e#V$W&p9;>_rRHDU&{QRC{hLM@F*6-Pl?)Ep59)&iOBW2UfPyu~1e z<$}-vBvNzQfU%_c%s?3wB*(E(6X`KIgo+A~P=qpnU@CA26-))zDKNT#!mwhA3hz`w z1Q7^2kw?nj6p#aiqLhVHP1Mu}aLq&zsRA_7L=Xv$06ND?QoKxQk_|vq&;%VyOAswN zPJ`A=5x>Ub&lK@%m2}Os1{f28OlxW_N+;1`sbr>8=`uQ!QAdXvs>*4uXfyqh`q>jxdEh z`|7JR@$%PAm5Hy{>$*J?FLoDgYJay_zc~|+>t=pDq*O*P4n8N_5in-3TD{|*NpuWz&`YIEDFEa70epzSYJo}>hWmmR~dY!9W=`XWC z{NW5gCmIhB_e`!R7QKm>l}4W5}(gkMOxOck|+!NY06gn19T~Pk;SeMwb|5?%{*hyXEqK z^+(~L*Vg0~{_8$C*i~-fO7Dcz(&vRFQkT;Z4}mlBq+Zs|i%mJHU|(s>^RjKLW(~7T z&2Qef&t9};TV);2Gx4-uw}}N$X)Vy(1ou?KOq3cLU>M%^4S=a0`%}nQ!iM@r_l@hp zVDfrE0C?Ib8z5Eu^uxu^6b`5Tb`>&zIGGOc+f~G;PY(^r58>6Y=S@9%Q9-6y*7?&+ zysX~0+3V|S^1Pf?XW+xSt=8=p?l{pyW!TocW>RgFhfZDJSJOrLxPG4{^>I?+OQxU^ z&&vj50hf3&pnuX-Wm`Ad7vGodW?8q(#YOfO8lLOlXY;n*Y##}++P}){X7*)&qIkNS zRM$ssrkB}8IeAm9r#*%*d-U)H=akJC=Z{nY_gcW4MSLW}e-`R@Me(~YudkJ&JFp0L zN(gk(Y}+UEvdM}w@m<;1rSfOuFNy&Y`8Q%Fza!-t&(2o0rH#m zq@FI;vlJ8@aOE=zvBd`oQC8o7AcSACn}q075+XlBh`U9Iy+w#UB_Zm=g!o&81b2%N zKM?XNV?YyN#2&$c!v~UKU_juKKCg%~9KP~N{i5;e!yj;t83D&kXQZjHwvGda#fDpq0ZxX91e-5c5Q=DHJ{53|#`p;~nA# zi|~qHF!CW9)2#_(*r!9-KUXU<2zV@@48v7;!!EdFpcYerO0H^h9KkN%A?(T+F?KPa zNx>20deeu%h@db=rFR~G5>A|t9Zs!C1t`>R;L2+%LV<-!#&AFj;d_u1Fr9bZa0iXE znARg4qQETMj0d4Snh_iW_n=dJu0e`*I*qej0{iivUsT3y_$Z-`l6}5o8p&}*Op(5Y zU_ucRtOnB^oJj=S;iJ4vPh!z0Ji|Eey0JrvEdYd01AtJ$mO!O{S7eh;%1>S}qGw!8 zgP~zWSdu4;$+KiMDNh8ro6%68DTZFWsV%SfS zlAj2WlhIl5iBWX0E-4%LI*i&4-!pD!6h~u(thj@5F?Ku$U%6}2Ql%ZHQ+nV@QUNS6 zsQ`vk1t{{w5{Q|9eTQWdEq8!;IEGJRZTv9XiHBd*RPXVy9%v)jXt8}L(je`=9NrBq z8^o6S5KMfk8VvL7)qs0f*U>;aUDO?o5O4B-@C69>?5f0_> z&LkVrU4P$4A2EzM_8I2klL#qfdeY*!U@AX}qz_aoDMk8Fay~kD!*Mn-EP9pt(^$Z! z645vrLmUYo9$B!Xe{VPw_e39-`-RY7lUsec=PLKJ1D9P_PmH1@`uFTNlHZHiF{|$* zF)Y*jUJ|l!>X0+955kinX2AYpad}xG-eqL`su0i0)v6Td)v_(c%Xx+0-<7M2X(@hM zi02FOVll((KX0~+WxW>9=jhxn#1E@#R*K6@ak&teOH@#xf1D!Rt+sgISAG_=rhHq8 zaFA+_z7d<{ZYw4=*)#ujGq2V}wy39~qvY>ZQ;T|CiS}JB+Idq|;u0GU zumtPdF5ZhR7P=NyN7w>@lbSr-R;xu<>y|LB-=X@;u3Un&YRfG_>KYoNY{l2&v3MfR z#W&)qc$PN3e-wWb--++Ve~TZ)bMZgoNAW_u6n_@~e=GhXeiDBbe*>er<7m_J1}>#W z|Ds#%WYJ7^tIK8eoGl!%&W|pu_6PBt2mQYo;@U#i<0)iHA z%FU(}%WjI*4yGgCFT`dcnt2WNgh!McrO?Bvrfyl6tPe%#*3XIxTnKq6J?yV9EOiEc&WW%igz=h3{Lm^nIgu7@ZTL!u7sm#zVLYrqj|z zl})=Sms6<2gADz02@kO@+g$?}vYnUB2D9v%i)vZFOSST%hDI;DGoA;T^liI&S3$kE ze{EA@O>e77TQ@N7it6#1#+*s7|21k2`bS$GZFRKO|7W)PTS}NX_3(s=H786D3~7*u zBux5T#)$|q4^Noba7se#!xJX17!xLA!emUCj0ux5VKOF6#)Qe3Fc}jj<2mhkPCF({ zMnfD8aWup+VKN@Vj)$;g!eq47(N;%WBmE60OjL2=go(EgPnbA=!t}t926#xq#Klt* z;vb$c@u&PZmzZ`0KYu^kR?o9nychGBJK3(o@%pqP=OM&>a8kOwxN*(eEx4;Y*^WS} zBY=1(XHdCz`d@K@8!y_lLxUH%_2fO}X^Qfna<$v-+uWqgw2%86+*CT|9a=gaG=9!~ zZbMGu;6ArtKIuNU?j}Ka^K>sKY2mG$T`Bug^<_u->(kss$bX9ud8Vzk&Vx($bLQ!6 z*4R8Kb>9_{=5y{uEv%q{A5A^Xoq3Z4d6wL<5f8@0~KQcOK?}uYZ?eKM%<1o!3JhZ49>@ZFCQH zw6S-vv3Iah_oY3hgO&LHMxKr9m{S1KsXX#3VJo32_nXKm@8Fg2sF0k4`ZL9E5F$k8 zDwWCQN3H{I%Zp`|pYR4=6S028CA@>!8YW#~W+_7s3v%)fBJAmjP%7j~UJ;?R%Z)yo z2pV?u$A5XOLpWK)oYzc$)U{j#Rxa1P8ykL3I&(L$HX-ND=SN{C%bDBuh07ztjJtt{ zcoHlsOgs))2Pl0o#{okn^I(qzmIZWKx_^%EJkniWcZ%2i;I&BgxLb^&MCvLcJ`9f! zyy|_9^y*iZiOuYC)66ciS9`8thxK+bseXL+_8FW$_UpV4mk0DrBMf$v3~*+hYNZH zhYNZIhYNZJhYNZKhYNZLhYNZMw+ng-9QFe+H8qzia0?&hgD2vRvPHZnFr zLNYTjHZ?LdH!(9gH#tT|MKn1xIWagxI5s{YJUK8nGB!a%GBYqXH8M0eF*7+gIYvfB zG&wUlF*rjwHa=YnFHB`_XLM*FF*P|klhH~jmtc7d1b@|46o>D5eXp;51zRZd45bsL zEkny(DA0kzEoCS(WmJhX5EbG=aiP(Lu1qkJkf6bU$z5Th3lmp2Zk@Kqg)0<@nBYdQ zc)uT;FXx{Bbk8}zbMD_ccm8p~S=bN8!GVHvC19k`aD|r_Vi_oaE%+8-Re>Vt z$2T9V1b?c*R($iY%Af{p!#5YJ7F06gJbZIl)`3a*mf)Msax!=dUo*a0EbBo7zCHM6 zvYY~@5<)M&87v#YG<=F&KE*MOrCu-#pW@JC`uH4tieoBEZG0X+#i36s=mq$8 z;$v4OC2SGCUHG)!#b60OkB^8-O<*a$QG5!u8Gp3kJA#jFlv+U>zGL{5rgpFl-*J3o zveW^V8MCYMG6(EV5GEB-GdmS zdS){5?gmHA-XCBuQB8tQBLa>nJ0kf=8-GNaBqIJuTSX)vX~eh

do!^TJNI+ z;(RtqCL>cIqV~85Ean1ZB<%$xHa20A@hG8lA*lMwfg&FOgJ1|`NnLziU)upj%zd~| zOUf82W7Nm>QsVXKK2o>XYVP#Yx_Jz#Fs~w|jg&UhLJ5sW)E?VeBJa2Y&`e2@(|;dP zFQu81ZtldQAtKF`wqog3vR31xXJS9-0b4*X7i4V)NHq3=wLnj-=N2usmyIlS^Cm3G zqKd51TVW6Jt^|D2vp>()JiGGU=58!?W{rPjT>HdXVO@8|Ti=pw-^)wK&0VX}k^$gX z0c{txM@bLKM`Rn(eMH3(@kc}*>3@Jo2Shp`ssoUGJj1J`N$Trsfj(3N7zMrzh{#u2 z)%{LgErJrL26e=%tucK4BrqEwZ_kkSPl1`B9x%*(1DL|I-B=t1z7a6~{d6!FP-M>t z_f+2_WsfX8Biy%wg@6g{8Q~sLdj_{h${rQ_W=g@H1A7i-t7`qsS=Gf?iGL^v#2W}T zR9Ue+Lp~*9jTJ6^sih)kUU`O_Uk8|a9z}R2q2B3cLL_F-v#yo4@QBS37L7xj9&FjDX)SuxV?&e1TbDb6WudyJwx9!zC5Ge zGr0XpE50yYp(3+@VndG=r+>cgthnF{U04HZttws8awT0$UP1-voJJ9W3I@awbe?P0 zQQv?V0y+ptARvLD-v9&>C|S_SuA>(r1qvE;vg?RO7D0zPVhB3QkwDPA(kZEOqpP5U zS*Iyd33Oi2!Hk-Mj^hrXLzsdFY8fbFpn`$o1qvG0T5;6_1+9~lpnsDjg#^M-K5HN7 z-)uNrk7QBMK*_>@6^DM)vy?U*$|tkqmPCVvgH}9zOILN)?jxs~w$)ZQ`nfEWnCQ^N z3lhmr>O4}M$ZjIBiNq!no77t*Hj(y36%s{B)F_ecM4l5VPGmQc*hFHJ4h#~TNNghQ z2_+^S7*r-TS@DgEwtu$NidTP^)ojH(=VY~5@tb;CtyaAIj;uB-HT219x6<;5vX)tC zpRD>alXKnmF}Z`9zbf zHCF!kinE%TXENS9CErG?xp`gICad|bRaT$X+`H_ocH)Yb{eM<_XOFYWV$~yUw@TkJ zSp!x%@?kcU@_1ydlOg+^tavuT0t9V2g^VQSPnWt s7w85nfTqAIup0D$UaNcMdfvh1cisQ6m+}~wnSTo*2rvpIB}Gq03WJvqg#Z8m diff --git a/latex/sections/results.tex b/latex/sections/results.tex index e764319..c724d01 100644 --- a/latex/sections/results.tex +++ b/latex/sections/results.tex @@ -98,7 +98,7 @@ In figure \ref{fig:two_particles_radial_interaction} we see the movement in radi Finally, by subjecting the system to a time-dependent field, making the replacement in \ref{eq:pertubation}, we study the fraction of particles left at different amplitudes $f$. We can see how the different amplitudes lead to loss of particles, at different angular frequencies $\omega_{V}$ in \ref{fig:wide_sweep}. We study frequencies in the range $\omega_{V} \in (0.2, 2.5)$ MHz, with steps of $0.02$ MHz, and find that angular frequencies in the range $(1.0, 1.7)$ is effective in pushing the particles out of the Penning trap. -We explore the range $\omega_{V} \in (1.0, 1.7)$ MHz closer in figure \ref{fig:narrow_sweep}, and observe a gradual loss of particles for amplitude $f_{1} = 0.1$. Since they are additive, a greater amplitude will result in a larger bound for the particle movement, and particles are easily pushed out. Certain angular frequencies are more effective in pushing particles out of the Penning trap, when we add particle interaction. As we see in figure \ref{fig:narrow_sweep_interactions} where $\omega_{V} \in (1.3, 1.4)$ is also effective for pushing out particles of amplitude $f_{1} = 0.1$. When particle interactions are added, we see that there tends to be less particles left in the Penning trap than without any interactions. We also see that the amount of particles left is more unpredictable when there are particle interactions. +We explore the range $\omega_{V} \in (1.0, 1.7)$ MHz closer in figure \ref{fig:narrow_sweep}, and observe a gradual loss of particles for amplitude $f_{1} = 0.1$. Since they are additive, a greater amplitude will result in a larger bound for the particle movement, and particles are easily pushed out. Certain angular frequencies are more effective in pushing particles out of the Penning trap, when we add particle interaction. As we see in figure \ref{fig:narrow_sweep_interactions} where $\omega_{V} \in (1.3, 1.4)$ is also effective for pushing out particles of amplitude $f_{1} = 0.1$. When particle interactions are added, we see that there tends to be fewer particles left in the Penning trap than without any interactions. We also see that the amount of particles left is more unpredictable when there are particle interactions. %The particles' behavior, when interactions are added, is disrupted and add to the force which result in the particle being pushed out of the Penning trap. \begin{figure}[H] \centering