From a3c4c44e6e199ca339091e13ffe1b56eb2e93172 Mon Sep 17 00:00:00 2001 From: jaseg Date: Thu, 10 Oct 2024 18:18:34 +0200 Subject: [PATCH] Paper WIP --- Spiral plots.ipynb | 123 +++++++++++++++++- paper/figures/nk_chinese_remainder_illust.pdf | Bin 0 -> 29064 bytes paper/paper.tex | 88 ++++++++++--- 3 files changed, 192 insertions(+), 19 deletions(-) create mode 100644 paper/figures/nk_chinese_remainder_illust.pdf diff --git a/Spiral plots.ipynb b/Spiral plots.ipynb index a0a0246..c0bdd1c 100644 --- a/Spiral plots.ipynb +++ b/Spiral plots.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "e4c5eb34-e32a-471f-923f-e572c25e893e", "metadata": {}, "outputs": [], @@ -16,14 +16,14 @@ }, { "cell_type": "code", - "execution_count": 135, + "execution_count": 65, "id": "adb7bd21-de07-4f61-8edf-dfb04b99cef5", "metadata": {}, "outputs": [], "source": [ "def fmt_angle(a):\n", " a /= np.pi\n", - " k = 128\n", + " k = 2**6 * 3**5 * 5**3 * 7**2\n", " n = round(a*k)\n", " f = math.gcd(n, k)\n", " n, k = n//f, k//f\n", @@ -719,6 +719,121 @@ "fig.savefig('paper/figures/nk_simple_illust.pdf')" ] }, + { + "cell_type": "code", + "execution_count": 70, + "id": "90f389af-0acb-461c-bc78-aa9797e4ef3b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(2, 2, figsize=(6, 6))\n", + "\n", + "r1, r2 = 10, 30\n", + "f = 1.1 # border factor around top plots\n", + "\n", + "for axi, (n, k) in zip(axs.T, [(2, 3), (5, 4)]):\n", + " axi[0].set_title(f'{n} turn(s), {k} trace pair(s)')\n", + " circle_r1 = plt.Circle((0, 0), r1, color='black', fill=False)\n", + " circle_r2 = plt.Circle((0, 0), r2, color='black', fill=False)\n", + " axi[0].add_patch(circle_r1)\n", + " axi[0].add_patch(circle_r2)\n", + " axi[0].set_xlim([-r2*f, r2*f])\n", + " axi[0].set_ylim([-r2*f, r2*f])\n", + " axi[0].set_aspect('equal')\n", + " \n", + " t = np.linspace(0, 1, 1000)\n", + " t_n = 2*k*t\n", + " t_mod = -(t_n%2-1)\n", + " phi = 2*np.pi*n/(2*k)*t_n\n", + " r = r1 + (r2 - r1)*np.abs(t_mod)\n", + "\n", + " x = r*np.cos(phi)\n", + " y = -r*np.sin(phi)\n", + "\n", + " current_segment = []\n", + " current_t = None\n", + " for xi, yi, ti in zip(x, y, t_mod):\n", + " if current_t is None:\n", + " current_t = ti\n", + " \n", + " if np.sign(current_t) == np.sign(ti):\n", + " current_segment.append((xi, yi))\n", + " \n", + " else:\n", + " color = 'red' if ti >= 0 else 'blue'\n", + " xy = np.array(current_segment).T\n", + " axi[0].plot(xy[0], xy[1], color=color)\n", + " \n", + " current_segment = [tuple(xy[:,-1])]\n", + " current_t = ti\n", + " \n", + " axi[0].scatter(x[[0, -1]], y[[0, -1]], marker='.', color='black', zorder=2)\n", + "\n", + " for i in range(n):\n", + " axi[1].axhline(y=i*2/n-1, color='black', alpha=0.4, linewidth=1)\n", + "\n", + " phi_m = phi % (2*np.pi)\n", + " discontinuities, = np.where((phi_m[1:] < phi_m[:-1]) | (t_mod[1:] > t_mod[:-1]))\n", + " phi_m = np.insert(phi_m, discontinuities + 1, np.nan)\n", + " r_m = np.insert(t_mod, discontinuities + 1, np.nan)\n", + " axi[1].plot(phi_m, r_m, color='black')\n", + " axi[1].set_xlabel(r'$\\varphi$', labelpad=1)\n", + " \n", + " ticks = np.linspace(0, 2*np.pi, k+1)\n", + " axi[1].set_xticks(ticks)\n", + " axi[1].set_xticklabels(map(fmt_angle, ticks))\n", + "\n", + " tx = axi[1].twinx()\n", + " ticks = np.arange(n+1)\n", + " tx.set_yticks(ticks)\n", + " ticks = list(map(str, reversed(ticks)))\n", + " ticks[0] = f'n={n}'\n", + " tx.set_yticklabels(ticks)\n", + " tx.set_ylim([0, n])\n", + "\n", + " ty = axi[1].twiny()\n", + " ticks = np.arange(k+1)\n", + " ty.set_xticks(ticks)\n", + " ticks = list(map(str, ticks))\n", + " ticks[-1] = f'k={k}'\n", + " ty.set_xticklabels(ticks)\n", + " ty.set_xlim([0, k])\n", + " ty.set_xlabel('$j$', labelpad=4)\n", + "\n", + " axi[1].set_xlim([0, 2*np.pi])\n", + " axi[1].set_ylim([-1, 1])\n", + " \n", + " for i in range(k):\n", + " axi[1].axvline(x=i*2*np.pi/k, color='black', alpha=0.4, linewidth=1)\n", + " \n", + " ty.spines['top'].set_color('red')\n", + " ty.spines['right'].set_color('red')\n", + " tx.yaxis.label.set_color('red')\n", + " tx.tick_params(axis='y', colors='red')\n", + " ty.xaxis.label.set_color('red')\n", + " ty.tick_params(axis='x', colors='red')\n", + " \n", + " axi[0].set_xlabel('x', labelpad=1)\n", + " \n", + "axs[0][0].set_ylabel('y', rotation='horizontal', labelpad=1)\n", + "axs[1][0].set_ylabel('r', rotation='horizontal', labelpad=1)\n", + "tx.set_ylabel('$i$', rotation='horizontal', labelpad=1)\n", + "\n", + "fig.tight_layout()\n", + "fig.savefig('paper/figures/nk_chinese_remainder_illust.pdf')" + ] + }, { "cell_type": "code", "execution_count": 155, @@ -1212,7 +1327,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.6" + "version": "3.12.5" } }, "nbformat": 4, diff --git a/paper/figures/nk_chinese_remainder_illust.pdf b/paper/figures/nk_chinese_remainder_illust.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c41597b0037701f6d1d32f6e6432eb363a3bb459 GIT binary patch literal 29064 zcmY!laB|#Q%e-074!pK+!XXfQY%Un^gVME(^H+G zv@?|URER}#jv=N8K<);)z9==X1nPYKpw#00(xT+lVg-=OaSOY?_MO}r6ID*O!efEv#zu1gEb8t& zR=59q_5Yu*=KFuWp8xmh+x!2{-u6FN|N9w#{>N|9f4;xZe+Z)D^FDqv{`39)eWrhJ z4@aNm{Qo`rZ~VXS(I?*i|9ANI?fZNGKGFYh+5UmJeRZ|=SGnK1TdVXpPBZ&>y>LnO z!TnpeoZf%;sp^tyY1=0!w!aV*pBVRf_wB=n-PdoQ@!Pi4?#Zw7`~P2kYk$A4`uE9r z6+YcZlP&hVcHe(=#(U)}c8_!)%LgB=XLFZ%ZoB+O)cvQ1Q>(i*zcXsK1$cExUMgH~ zxYbkh-T;@8?> z{{A&b&93A=-FE&~*w2^qemtAIchTCP=K1#f|1OvtA{| zc$FykWUGDJXJ#?NbxkH>U z%irv_I_!rO;(KkgL# zJ8UkW_v5$x|1aVDe?G1M_4xjuPuuH%d~A>Z|E<4%$KNmV`S$g{f6lghYQ!kMc=PG_ zI+q^C=xwbt4c|<^FVMFzU)i25=;OBu!CL&xH=nL&4_dHy!|T&JlBfO}w@=bbuKcks z@RY`{bwckd_WeEmoBwybeEsy*TR9g8e?G9R&AK6Vf5*H!-~H|9p86#x#Bb}&Z#w!v zOZxD!+Id$^-vockxng*L$ZnuD6S?>6*9KGI4fBgyi#z z5I?d1pXY|z-A`T<$$$E-+~u0TqW`Pw&&^Lcb?NQ;C25cLK6?G5t>X9V`FG`XZyR?v zO>W|B+HI8j=Wy*dp3{Ez8`CS;16FJh>O8eEF;u1hyPdI&OBI9dVfF`$F0mYZt?{Sy z!NumLsXKygm(5tRO8A+W{-QmHL|^@I(a3t^nvq=Xbx7+$YzgDWI*B(1mfKtG91ihp!Y%bnajONaLrgT!LUKFt&VSbrkc-> zDIX=C$pyz5D$bCq$(i8W<(gz=CK}ClT+r@Hi?EvEIj)ddelK_M^Q3vrtJFwu2zIgj zx8(NmBvB>tDf{17C0#u8*djrw@RF}w>9wa>({{|0E7A}3KQ7kBf8y(688%a%TJ67^ zZ%vnZC%I<+lZSkNWme9!_z~D1Cv|*p0-xd9KOrk-1emf4?q-W-_fuNV*0wL}O@!&0 zv|N$Hyk~jmEqJmaiS>W>b)NGq@d1n5qk3*R#_&h1k2I;UXugrZ)orc(m4fY>9K3Nl zW|7yc(%&%Mp7JAkMdq0u-`wA=)edT8Zj|?}*>&g0q=$DhzBJC>(VMBKaju->>QmNd zcIGGDS07dTDf@H&tDHFh6)!KVtABZU+y2DFbrwt|H#FLnZQs5w&`P+q;P#i&h!zh^ zb6(k&yt?w&u9F$>?-k22@{Hy+F5rCeH27yxo7CTmHws-F@4Bx#e8gf~urTB5Ahmhd zOXo=U8GOIhAUyq+#GKk0vTG`z=!B`;ZH^Tp>&oIH4$B`d^^ir&s&mgmSFGjY*k&RDkh z6+SjB?cB#}`RY=hdsx{db{NlDmB213rPmtw!!qE>g|4~rmp3-6+Zk&X95UWzBKbv5 z#L>S(`3loCu6H^|c@9fFcQ_NeVu)Wi~usg}ftA#g4@)_XQQU_OKq_?|9BbcXwq2-;4|2VqP^$9!Nt6L)e8ujH8teYRWNcHV=VdBgX#o|%2D+fAQIJXfB% z_GuT(A|W1K>nk%&M9PmU+&IV^-*L#`-(s25*Sy=S7X(j!AatWx!1CL<9U=#x%Kkdd z%aT*mbg_}|l&F?QZ_?vN8Lh2FqT0EFCYOHM`dxouQMgIHWOAjFYogmyN1YNyp`JCT zA7+Z$u_yk@*phO3`wH9e=AsS1+ZR^OY;OMV{Ppn1!}b#YVrNL?NglMZ*sb{6CSm$3 z%OCD66Myudf8HYdEbp+r6Mx&D8WEOH2Ny0p!7r!(B>rT8UF~o7TGuX)r#=gx-;0jj zz37}=r)B2iM5AZ7L^Us}AL#m|5ngP*Q~Sa9uS)mD-A$)F+uWO2zDu}Z_k$}}xBi&% z*CChda_GnZr=m=B*!jigCf#TkJm+he(wCs$JYl2iaZm1NYY*hPYi8$i$+@r}Ot^Tq zF{OfYwdl|4iqao3w{>C)XRPyk-BF87nILun~~;ZTyjguEay{X z^D~80LM8?hx$#v#Fb+CQc}<@ixT`%d*Ud6^dMy@d`=h`{S?2bW+1b}W9d7#4 z^Ft%^zxa>ENB`>Vi17_fY_59KzC%G|iNx|gue8o!g(EARy97@6amQL8sVmxTy}#hu zL;i#FrnGUEFhrHP3-G`D@u15 zPCTbKXUC1@e)Z|w8W!#-dDape$Z_rT+=Eug5wjwEYfxhVR zi+2nzKk)k{W3Xt8(@ZT>@y{<7b{lV1{U(zfD12C1GI*Y$8q2;Ve9U~A?Te#k+dP&s zP`+Dc`-Sy$;FifIC!^x4ydp%_F*5G9xO4Q-45MVe&x?N>T*<%msNGLtkCNR|aYaKJ zmL1x^Os{OKiS$ta>Lc~-aof?7(1y&`+{|y;H(FM-rd(j_*7A;)WH2~ZrTD*U;gjR} z{}n2w@0^_E@6-L0)$v?r>X*=kw|Dq2*WPtZa;f~4!eyr<7bJ6jmC&#Xzk6lc4cR+v zx(D{Uuw>p6U3j-8zCC`s%kIhf;VTvha!Ou&bDB-Jpeo_P8PS^)I^1GkxD_z#ahM54 z8dMiPkl`s@btz9g!lf@cXX&iNRR=U~UTHjfN&3yC!h0K@PSY-EFo~R)7?U^A*=kbT zyK{dy89%{XEw9XV<^^c=Gv2EiE z)vPx2k~OKnLe7z%gm)PIm>~)19 z-R))7hxr1G^HjcloO=Exqx`+4><|3+HKY{$sj5D9I-R}lvR(P{J)F_)Yghghk8H`N{0`0)F=-tzwppUov%=S$W!C2e@(H0xW9y=?1D&V+YQ7#1cydzWj| z6uV2cO#e~y+zs|Wo*2G4e8ZFf_X7X6BmWxJXD7|?n_I0oL$qy0-|6*<$F(LNtg9>% zc%tC*#fVQwJEnHg_ungKx;HF-(s%XOq1au%$JOpV%d7ricK)`3-s(-fRndpvGH?G{ zx6688W%~7;pYP;rHplId2>S4M(#q*eHD{gHU8(<{(eBHda3+SDvS+E8fo7W+7}w8B znElL8`^M7WmvSCWUbn&iM~Yd_;T;Hb_Y2Lh?%?*f4Bl^C z(l+mQvT$s9)fxT}9zAiMlGBy)MNJFmOWwQu^mExuGx6O&=Ir=;@VQF<;T<|B&0f?p zp69h_)V)5ZzC7*NJBBx3dRji1 z)Tz|(@(ogy%1l{YFFWhlH$iLhgx_t~TY6n?NJe{Ay|NB6`)2rNPj9Wje1-f2mk#Uo z+c)n2Xe*)5f8xH#g!}iLkItJlkzXj?>GG$o9C4c6$7D{o^gHIWUhejtKV9NsmdM{C z1Hr)9zGjx#<4Z*U$UIcN`?TY;m7{3hE+tVP%gv&m3?++<8P6VVO;gGj+bep}nC-&h z62n8EWzIZ2?AFUvl;K`5XLF%7mr`--C6lJqYj$U|kGSa{p4a!;M&KXML_34Usx#*F zH29UPsaaT_k_z;Z%bV}AQMprdF*kc^-HK~YP7FI4Kh&jdxnEqwmgXD7^v6!S>G`<> zVZApKY+QD1oH<9!q0L?)Omiz2cgh~$)gdjce7B5vCtZBa;p%@}G&C)bx$O< zg%VgFi=gQ&zg-v;HeA@K_vFXK=>mmSZ!|y3J#4(9VtH@o zo9vhQlN&;&I5t?%W8r#kGlggVv~$`U!}Mtt;^)kj7vrNaV+GeH1R)gBZTZ|TQJAO>c zTjCfKx2C5YUyIcF$dOZmeR^V89dB^!9A6Zni7Me;`3fMCd?nJ)N4wtv-g!DOyTx<_Yj#$FN z7+fHgzF_)gC$q}q+iz6!-dJ-+`XR?eO{Fz6tda!O`mKrrX7tS6HPdRytFl+u+zNHE~IA>qny~5^KK-l!IMoGJa30`{*Kg>R7`r0{R?kDjZ zPm+#&yqx~h+mC}q_N5aN+z zaYoPlto^3$LU*T$AAJ2hJzH-Ezq}Edx@l=klE;%N?2GD?PZb38<(``P)XG8rSR()V zn2XbTpP4JI6xM4$yD~}0alggBldbP~z0^(>wHW9;&9GXnaaA!a&8UdMoafNhwDwRMF8KtAgIkP<~Qamamx$q+>-K} zX<-{X^OeW1_~`TPFL~NJmIR%W@_nfyIN_D$FGH~zJt;9-HMuLiZDu-cU1GU2ZtuFz zlZ!bTdFLFv@N3qwG(RcF;$8a5zSd#aV&rE{+IK|w*(}euXHwgL2h{{_?E6&MvFWkP zan<&1FI|j`a`IMA^ITk0ma4Yt1n)VYhjC3mjbl31w)Pmt*fsgEDt{15|2p+h*vhc= zlU9EAxL;D)p6>Er(RiZ6uetKAE>^P+h6VgRy!3{^Vu_r)57(>>Zc9EDBED8k%=Cx% z$-fQ9-Z`CO`h5DPzxEp6^J?#1*{}GSZ#0mbFv;?6uG{qF?6WDImJwO}EiHLzxJ~EhlFQd)Js<0P8&t`b z{whlwq#8PISv^=f1&Z6KX*A;_@XVb;}G?&fM zc2pM-Y828;k`mMVb8l7i6nbeHhcX>K zv+D5KvzLQBEhZkVDOpiEx@0{gV^FV}y7#HH%a3>i z1GV{A7e3Qy^PPY6$d79Yo1M*cYqHd4&Jx_W?4beg(Df2SqvvO})p4ss=?TGlT_DiR( z9A2rBzU8^frl^w|i*`(k)6G<4?6gxpYOwa`pNTHdtu&s8zc?moKgF$Cb7SJkNR7*{ z`15V%nOvXp_<(-p@>YR*o}v{Ar@x*qy70SqT2ss2ExDej8NbTB`Q9OuCG$?ySSb5j z^_-qeZobowckkrR`M}UrdD=iW;;N}!MTT*B`LV*Pk{S*F*B>PgFObeUd{A>E>zOa_ zp1cZ-+xY*^^5y0y=4Q@6o%8j}1je{&4~n0yTQ10TN1!ERGLOFM>|*yO37_!Irj3e+ zCg+K*6p@*bw14?y#p7+eWY_(;r8wC#tUKq&ajuZuZj-BV0quty=l1w2wgo57ENKm% zDJpfVE?|%LpGEI=@&X>&d`0F?jx`JCTAeYlUw2m9*?-*@*?%in%q;q}ZG)*#oG9Y*uhgh+3pkuE8qJ|M&fp zKU{XIn=6hidbDy%^#&F*lkyFZ?|jjp_0P!FVawG}p}E3ZQ~96f|6A6vjKi5Tp+J@E z+xn9mmlT*c7an_QdMobOwF7*o!zyDI+J15pGBEngdg4~I)>WgT#haEKD#};1X!LuY zmQuC3)hc$ZV&xfq>hMpgsjHt!ED#!X>@ResbtAPu$J= z{-j8Lu*RG&L!*sP7K%)Nd_tH($dmJ9>`T4(Vt#?52kLbzZPO3=Kf1T@l}6Zi#|>&< zOs0q&$WqcUbM?J;wZX~Ae7er`U3K#lawan-&9&a6YxzuB)qiED&Xb~?oO7v*nAV?N z6lN#S|8!bwRa(IN^Y2T3u4!Txo7VI4>(1Ce+^s??M`uSVcQ>cR>E|7HnVFdNBvR37 zW67I@K*#vaJ;}-(z5fd2Uq(zlRS?e@^tv)JU~;N>@I#R^hYeVqx6C?JEXPsNlI77P z^1{HT$Ms%uuJk-jeim;<-kaOyz0I3gr%dLV^KADFQBQeT%QV@Pul{|p&THZQNd~Gi?mk_3rq-g($9KPO94pBkH$~FtDim1O#C z$NVDfduFp&Shev#6ZQ+;R(R%2rQ{Q@(t{^XJej)AvqapKL+;@eftup;rjrwoOp$uJ zhUxSC%M%n!bY~UiEEZez`+bM&iU5sv?kPO1{2>t=@?E{z-LLxyE|xeWY=8Sh`>lqg4UR9Tj;cL9M;#y%b$I&OY5R zZ&4fDwB#et_NPBM#l`5@azXs?v^|%tPbWRxBxQ0mXNO;U;6t5985iPsiXC>yE}vTG z!sc+W!xf%$1i(~;cNb2?X4mo(3v8o&4;*U_glKe|l)-B_G8ljpD8AXSpX#4@b>)Zb#cMWSy~YeHBeskaA+lS`($274YRPq-bNE@(k8qwh zAyp^mJov!dXRI(UI8jD^Q-}gT3r~?3o0{SE)CC%oS51vcjY=02Zh7~7ZSs^uhdN%E zX-hr*sUr2fM{<{g=C8`O=vgmkP3*tj9N1d<@1uF(3D2axY33UJ|Ckn~=qc^(b5TEd zmE-I3?aWDQyXMMgDfH~nTd{PjL9D0Z5f8qt2ZE085O~b+S?QJ8UgaM;ZRu{)zAnuO zl$MJWpT<`m*Rj<3PU06?@ASJH3Z8i7-Z&MsXX4TPV+`tDvwaVSohzKH*8X=*>cjbK zQat(Q1jveo|F{t=#^4@RrhR>Kd&lyW?vjlz*J>SBPRvSOo-*Te^jSUDY3j!^8_n&i zmKENMBZtqUxc{fKLox?g;{F{X6J z$)pOW1-GB1iM~<`spi{$BI2fo+Vkd4nV}q{DUSW4TS9i}0WicJL zWR<(8BM&@0%`GO)(YUJ7a?MK<`<{J%W^dR(d!^0cP2-w#F*~$c%J#72i*u#yp1;1F zQDok9Nvz_K!mUEXCiQDE9elB64JI4)P70;@3Z`$1F&8nk+4wMn!&V_$YngA8)*(%O zU8_w~R{UaVEmL%& zj~_9TRE?5lRy`ScIee-^!iLK;SqtV%?%Q>$v2c!I`dvl?A1P_2kduZ#a{3g44J4e5 zw=(>FmOVRiuGG{wO;U}s=CFBfcrV#D-*@i@sbkmX+>w5C`PiJJe&@Dz=-fDaN+D3L zLuXAyLdlEWX$m}hU90O74`p)AR9(KUBIT%FP6vxb-=+dF=NH^758GejF+P@bNO9K; z(f*qoB!5+;o|K+bDOYkd?&K;_-Ve%qbS=9-fBSWH{bV6fp~`2Kr0p9ix1;9d1Dj<_ z3$DyQ`SPR$+xe*Y9G+C$6S4=(HgD*u{263Z&18MA<|Rj|@UjhDYYcQZGeq}H4Q}SR zaXfF|gY9n1J3iPhdeZsv+M>uWaY<%7vRr<-nDd(@{+_u?CzSWSPxv8^!`y7hfpM5x%;WbDQe@tc8muoTILMVT~wM?RdjyX?e})@R1wh zfhGD8!BJ+?Jgb*lSu(|(6Ipe&IharOz~1%qge#JYKPvd$dRk<7w7_9K=e+7|DH*9V zlS(X|94&iX4!D;w%#u54pki^kzHyetf?HaxTJuhcWMvoG)kOp=%xJnPwyx2C?#%>? zux--!!hRl~Ja3;!MAk~4>HgndZ9HT2SiGCtQ^n~{An$zV6Yn2tD<*B-Fj4tVr_&MD z_E4XryBiK1j`+d7djICB-hDQ{<-up9@?Wb4CCcS?ckE|LO}kk-b>+JAbMFcih9w_L zI;y(7+C-;%euT>&JMmr7N4ru^v#oEuw&mk}nP;=lF3#~QK6%-C6VJChmeW+XXU0yj z@=J*<(bCvwvQ|(n+4Qtk$h0XBnO7M;-B9qYBGk<-vi6vZD4Xf-n2qa2S8aQuAoX1> za_O}g_Q2-X0h&|YR!!g3wt2>}rNKRyP1YV4V*IAuDX{C-UqR7^T|VA?+b3U~5~csp zLBizJ{cnWWH)oV~-_qAy zn)~&5S4GmYtVNS=C(NAlZE2Qk_GXv<)!z;W82V;E>X4NP-ZPg{9+XxN57OX4p&$7{+=InpPW`I958R+!h&yVxA{eqU-a7Dd789H@N z>OAtM=uu?Uyp5iDyo+TgZMYNv=1jh>T3j(t=hp?Ut-Gci`e!BdtG*3)&ww z_8g3GeJwBGdFa*Y)V8f!M}JoCoh6xYe3i?FYfp5R#Yz_a*m(A3)5QBv=GAh%t!79foePRL zzHFNzb6a8g>P>%}n;d?ziKz%)lRvXS+B83+oay78AoZmV2Nn4O=Fkvan zGh~y~X<&|>vFXxP*Tk;p50A)xm2BEo!mx(_@N9v1{w~ulf6)Kqzw8_bzXHQ%ktQvs z9@bT>gu@O+1)G2KmZ{!8FWAejwp>MgZnEENmPvDT zCe4UDRg#k;abx${4PDn}Y>RlQ8nm@1`Rb3*##^1sGY-8pJ<}Yh5d9$J=2o{GK}o;9 z+&v>DnY1D6;lhe;sY zHRH5<#{NYMZe5b{DRI7ecF} zYKNZ(wn)9Hxy3)V#l)z3{kJwzm4#;}iFv&E)>%~bx$U#uvz}Is4NVL6&z$d(KYAwd zsOyZfV9%c!A058k*{~`wa{jZE^UG!=t(#Kl?6*1hsL|7er#q)EuQ=kGYdM$c)XmQ} zakU(szqJ%CYWXIMzvkQVQ)5zc@b34UVx;y?J?FZ=%0cQ$g7Svd``X6y82RpI(d4fIwHC{jeJuC9-}6B8`|O?VCsVuJy>9)`so<2Ci{C7GDA~M1*W>xd-LXkx zQVp?>P!{d~ia$DOK@FUop%N_jWTx~#QbqPIae{b15k z<7JCY6@F&jTW6^7QufE1eH$i;8m$uSQSJK1FnLt4t8 z7xiAx^3r5KwsFzpsH5{|YiGq>EJ>ZW_Ue`mLj3zUJ=9FE?>_b_N33P;y|6R;ldAuz z9JoGjyS7-vL{65-fRl&#P6_P3pq6-8ii_J}*Wom2Gsl#ywxDS>iIT0Belxx>3mLv> zUSnYK`J+RCjOM{tn^#BKoha{HlOV3Brt!JKMW*xOI_aMrlov?pNW=8k=%??g!Y0jLh z@10e2&9J@1ajeNpjOpYTy^x;i2j_OE-ptN=w*+3LcP zbg@<)cAeE9S+}q0p4G%teDIr2ufR#>Hml86OD?s)(A=%d?efaDWJ`MWxix`P)TL@) zp3@Ot`8TzyuIRMaMiB-vD;>8Rr;;KchOb#&QIxuuBlnQxcdcW_-eNbl9gLK!4(s*t z_@*8I<;&F88ryezQ!Ly;jfWT+zuj`YNr@ z3_qWFB|k5$`R+L%)29V_y3$)xw{fmH^XlEdX`K9vs#1+NM?afWbml|NnJurm8lLD~ zoHmpH)=4+#TgE^CX!Yo*F1yiX33pnA{;quca%ImrlSza_vRCaB zYOjvPaH!-}CuOEvZMc=WA>(&hs+)jE(=m$`#oeBQAvtD;l|MJBdU(bPulM2gJDIV0 zUD5WVZxTxX_AFex$?|#Q2ZmJk9x_FLRYW8JeBzH z*YXMWkM_8HTD|JAvb1~K4zWASewBw@ZsC3PvB?5svjZ@BV*M8h_)V4NC{^8t(Qx<919jm%2;d_B)@=*tF zvjQfOZ2R<0pZ9!TTC)FShhMAp&rr|r+APNn{OrPl_U^eXWByO^`C!>uddHi379(f%u9n?o>HlT zPO4X)TGveU;q3XC)m5rAXG#`h{uVt3>CUN*#y*=&LvMJjXFBk}FsksI=cKbqUDv~| zHI@afJ@hZ8=KUO%nC30BlrO2LhhLa#e)&Gfz9U8}>|(twWoI1ll87_eu(ADWN9$KT zZ*!@eGycZhIAauceTko6*k%c_4gA;l_@!OD%elt?#kzxY|C~AZ&w}4lcgLBNm-cWf zY&enoF!kKpXGa+mt6m=QJes!MfW`5ya5#Huv@OrWt zYZpE|rgHvGx5=TvfLBL8pLz8!V2{WTl~uv#UR10*<)^+a{cGxrvV#{+HoIFKjN;^v z_rFzhZLj*ypXd2!)r#HO!BsLzR66wa?qg~4@wU>S2FAA{wm!+pFH;U}{?k}=@0y`_ z)3c{Skv<=ZPqyD=po^l-8a56tM5$)Zp?vt_MFA@t-;@bC2(Z4*x^G z1K+p`j~2%H9g;nKJNpGn%XU+P(JslreSSb zPo&6-&s)5N*B?LIZlg6DF~KCQ1I$7k)GdM)hca;v|g^EZbwZK|8rx$@aeD45cj?LP{Lll-7X1!6rRDpjDN;@Q!`TPkCL^^dPK%c7;=c(X!LwfAuckm|-~o^yYihpQT(_|6O>;tLB-FGtYJ(-CmV6 zLv@;@_3k%o?9=9(Y+LQIPB3h*k)y;7tNdT3*UVqf^ZiyEIqT@_h051iCZ}_JjI=-d z&EiH$s;Ke0s@EsjpsOzZ_3%t*YaP3=tYpxx;b&uYm8(Mwo>5Fb2 zdepi$s_NLA7QTs))?envBY*Xqu-d_&CJa^CtOst`&$)Xz>^Z|U zcf~kA?TcHicm@1Bx@)$VswwC(b{7a74pU}+BypE}^7eh~BA0Eq%%5K?#4oOt5ooD`tb71r?aN>j8 zKdY6hUY`-F>~{P3tS4PrTv4~S?f5?Ztc_2@|GlkETEsQeJ7&Y}SK7k54BOXSzt*lM z6ez8{re)XmwSnB8uY&m1!lp}ad$Q>Mm6(0I9u?F^mA90?@{lX)XdLo zuM08rIi+adi{3jkgVnHMAH%7ur#mZ(U))q$x%PW-65qxO#uL}HyEd3sR`u^)dgGwZ z_t3-DTNX{)sCQ6$>fE`jOFmzAG_$mhHPlP`v%#W&wQ*R|y$N4Sw&&~5-7;xWO7f|9 zbGNg+`Yzf!zjxP)*Ji3& z`;wm*C->-H+9h26O)l-s>uV1a-dy|Kv(!J=VsqN-iPLV%U+Ao=_BYk^Qr3U3d!s{A zelP3xzFZ#9KY7Q!+qdhj3bU)aU+He~YmV)ik}3Yt%$8|C+)S^RzBXIVeg0I$rK>ah z!nv<*G?;SrcwhOV2VdEf_WZghde={KkKn_b>g!)TieGM(Tlg+`H!6E7 zemUQ^yLWk}?A9B*|A;!q>|G<)bWSQ*J0vc9pV}pBjndNyEtL)(S$)Mu~iJkA%0y-wR;?!D!de*Np4(Gvq6tgy8GmXyMAGVaR7 zr>o18g^f?`YI(C(?q-Nah2V#4;*;vOO=rlDRgu&_mr@)3ZQbNG%`JT=UYD%boBD|R znwZ?~s7d-Kcupsa`>>T5uxF-5<_L|DP9|%-ZzePxOg`vYBV6U3rnIYOz;)?TyOD+z)qr zzo>1SlAN0(d4Aq@ke_)-%(^uZ)AKX(9AhoAF220zeQR6JhU(|r?p?m~YsQ1nsJ5}>{^WW;!!xOGfO@A%6zWZcTIkVO5)5h`FX5Ho4`+ZURP7S7j*|XP{ z*CyTy{XVIt`emuVgN|DM(yd>Qo!9Zzxg5~GcWT{rTU9kX>Gzj)Q+j^vwft3g@I>^T zb>f!!jMnRzB)*>1P5AgyH{oM<9%J?UNvpo=%{>%uzkmO$!@IwSKlI=CMQhFL`7wEH z)gPz%-{DzyTZ!qm-M91mq}J@)BekaH`s#y!ju}t&u)9;1wkf|{Qb%>RL~vI94$czJ z8>dfa$=!SU-|K-Z&$j+`r!-XNC`$y|Y>c**9hXuGeQh^ZmBVzy1^_tNZ7@{i$q+T_0JxPOrB) zXfIkM=uxCP@j=b1b&j6DO*Q_1++X|q_5Hse!|neqkG~zOQE{c$F!b70)i)m&b+^6J zz4O=Q|J}0WEmY-e|}Y+Klj-1s;14BgPZp{9XS6j*zd7p@7{9NfIao{k zfAX~8=JgML?D?2D=5f45!to;^9!(?6d2DraBF zfBn7u`p8{#TD#>#r%2wPv!Z6_iytqaHq1}V(J$XwxBva!^1FGLzpwp%H2?pPs^{s` zmFl*zXS8xjtG+Uw`o>^)*AD}~-~H^-@)uPvC%E@s`?-IG(*yzSqpD_$HW+>C)x3Oq zvj6G-9}<3jSsGXO`(j4@0oTe8ZQp`FI`8?i)c=d~{y)O+P8?tV|IO~^_;ZicZ5m$p z+rRIq+cW=u^}OHr9ECrBe;;?cdQSnr)-`VPo8LaXUBCYXcm20(vETMNm&6r)|H*gJ zJ#J@2m*blgpTEw2bM&?Q$9T>s{o>od9QQFk|Gnn(a=wfmg`)dUyj+v!t+(!V@cQE2 zJ3qzT^8NNNT=7N0L=na8l#{(wM4@PuQBC8mAI=2e>XZQA8h0q-AI z*$!IYu9*C^RK)w&)wYXAYHK7~x%dB8nAe(@?|mERV%FU7x~vwzG2**1UeUV#T(ywJ&cjUUuX9j@tn*<)<5(>wi?`vD%cMOYQ%kgy z8r-z!e&6=t;Y#-Xi#pzv3rc?dAZL}|w6*=P$%MXRR}DX{x3&4`RPbldOFRBgJ#U_` zG-fDB4Zzu*5}yj=dnZF_(D-%9?5 zTTXMtS*QJ0usdzoz5e)y#e&ZT;(j_$7p&>CFZtNE<+0v}L;s^MoJoJPp?_nx_y?PP z#w%Nwok?nS*_Fu^Z?OFOnWs16_j1SYnRh*HbLNxuy}xhvRq-8scS$_IKPx@?;G6W` z2g1)^%}uQ_ZPGipGHK^|se}K2eEt*nO<|ew-Dw~6m8(wdajI=@7J0c`^yU9&E_?R% z3qPvU*Fcg?8!``7=o@7v7^j}^aEm^Lgt-B)FN>2A5n&htqMu@Q_Va&Ja_ycc+~>cazyFW_OCdFvmav zvdKGIAr>xX2^F)kQP78OUp6;aAh>newr3~r0S6A2;#CV;9xqooT~zSS{;Oh(aM>1q znNIGb=N=01#8(IgnC&xo#%AUeZtwCh*zXsE=HkpNZnON(eXVHT;T8o8vCV!lPbx37nkBbw@H#V5`dy~@ z@rv!WmPI)ocR4qAEMFe+Ys2k>R&r0ih^^i2n*8WUvn<=_x}I3?7R4EKXY#^zQo+J4%spzj3Pp{{FaU}&bG zYiw$$U}$D$pkQcVW}y(v1&cQ$3lkzDZlZS{vjPw6_c@2eJ6iT1s8kA#UGn{Yna`zl z49UNH=evh^teG%hF!8(CHkBf;7t?0woqzZ;C_3)&_q|`v`%Ur+;pZ$|mLcO=x^d;C zEgP;bed%t~QPC-{zF4K^o|M$ni8p>t``ci1{CkJ%`j7>eKHb}7(ffiiPdxJJm7`O# zTCIZ8A3I5?eK>**DR)vDgChi0hphZe?vui>+HmopPro^|ej_M6}TrFPvHeRYqw zCGXg}VCL2t7N65JydSln)G%y`i21&T&pPZ|UZkeb$x|}P(ofI- ziaUH=Upqh51WOEo_VI&q4k#T$PDP+Bh78Tj2*;4=goC`y3OvmJeIBw-5Sk<~V|mb3 z_uc=u^DSL(%(sa-SNo9gd^6L&s_i$p<=lH~r}{VZ>558QKMdZ`GQ;EG;!3^?pHey4 zI>qF4Q|4{%YgSB-TGme=R-H`DaRD z>%0w5j=9}`#=yjDOt-!CyYRY4!075RB31o9Ec zD&NGCqD=5{5PAj%pd4zTU;t;uD(Hh82|A^sSiul{gantqYhH3b_zVj~DuD~>yJV)N zr52^;fsUMrRxmU$RnX5=(9co;on4`zAD)>~l2NQ+2ssP`akvK9lbC^t6b#^CA?)Xz z#PnhXOEWI8a=gA*(043O2Az~)X=JIO53&iw(KRwQ104lY;E|e{o>2mdod_6HLEp0^ zF()(GF)uwQRlz_(Ke!|{Hw?t^O{@U>Ou^9D)Btqi1*}>E`4i-=XazF^18QI{a?LR| zv`{cHFjO!xGf=QFwoouLHsi81HBd0OFi72dT%0 zxy+2s!1Bh%<_aJTvIB-qjSUqH4L|{4VWMDWVWwbaX`x_lZlGXhY@}dnZmM7o!lp(F zMwX^rMwX@uW~OEerl#f!7G}l@<|Y;j<`(7(W(LL(8YFLQs$gbls9JKF*9Qm1tW6{Fg7)} z1k;x0CJG>NGeaXTkUkJLF*H;#H8NB%wgl-jQ82YMQm`AV7fvvL762 zpa3#300k%)$WBv33rL`V90tSS^aHlV094z7f(RUJrtq`_jt`J^5X@z2X`leo4Gv!f z!^lv<1Z;$n1z0QCRfdr01SJEI%aF0Lu{jq=Hwc4`GBGz)Ff%j}#e*f2P(EkOwr6s~X#P7k0o0mI<50!0F(~Uu%#t5T^K^rg&CBFr3n~qW(abd z2^W|Kv5_#yez3SPG~GaHP`UucDu_n3L_x(VsBi!kqnQeZpoVD>sHgny#iSHX8(ZC>;@LHj)y7RX&O)#EfT316J5X_CC^cm1X6KRredvV3B5f>u|{+r+tq zzIegz-l>#4UHtiDN6wdChcco%rk1-hJHGq0i0cBJ`|MvfS&?ylP2i0vmRFjgGne+{RSa#g`G0AkXT3vck_#YkrR`)||A9#v1PJb9z z)^u9>SgJjrvHYItVds_{o6K{<)y&pL(CCJ$fR({+w$dAEw>tMJKHRJvbk=R!R-jb*Kp_lz9sBeR{hHJsc^^hX=@IoJ{FyPG=j}GaHqFn?Sxl3 z3)L6y(U{+yW0%$8GF>D6LFd7P8W;H9?0lR4C{!^c_U`iB^@zaGf zeVfTUv48dF_wKv?o8M0{M34)kD`o^r$FO7#4KOnc!r^6Xwk5zIz`#8Gf~ko~sDY7D zfPslopoifTBNG#L=@es>pmAnp4XPG`X5w2DHq7Ot=3I@e}5hGEX@F)x^2cP7X%yKc?_ql zf2_K8!Meu%-A*6#9=&cpq_EmKNa0)+e@DriWo8qFtz_pI+b5bQ_Z@IGWSjG{WSK3y zn&t09TrI`Ysc*tO)H_!x^}RCg)10SOJ-ad>}_TICzDe0QaKf0_%hhHl0W-Sjxx{xKC0Hi;Ix^DA4ppRGj(- zdUi1z@a%pr`pZEvZt|Yx&NH2#|G$2Uuho);bN!^r(`H0)^BcCv>)8I7s90?NSGsP| z&E1hzlTP0JKjXPlaNv)i6?#cdu^rOq7Ycr`U6?HtxpD7DOP$3ti}$h1x9(suUdWhS z>uI!e#j~l3!hSrZGJH`>4(-TJI{YZ=qD}9eyx(qVscJ2}{V7g&BpNytUNdcy(3xUp zCTtXWj`=O`N#3Z0>no)LyPLG9T;nWR6n13QnFpJnT`Mzp*8TKgMeWC58DY~CS}%Hk zji`ukwVSbWX4$(*PE`+mt(DHmaV;^j*45rxedJYM<1hQuK_C8}{Qg6BJ^$H1F>|nl zAn4>ev^cdSB2Ha<4+gLxb<1CEa{IUcy#hux3D5c7wXkw;t8|lRovIcm z8o}%{xnkD*yAPt4&x@c`5JxgQb(rk-y*tfECr<0zz2hWjHjGK8H zwy4f&>PT;xp^z(ZR6)#TA{-fM-Lg{;>!l_*)!taA0Up+QQh;v1S zm+!P)+*Mb$?7OlrqF`ubY^)Fq9}qLPKNo%`ur@HPJH{-nE>vpXA4o|5G_`zrX(Pc!R9yLO%Yx8(Sp zHP`F3--IS+MtYy-+&*`Angi#ZV9Q&pZSCc`tiECKE0(qcF-gX?XE*Nw0}hw!WeF^G zYTxVvryRPspI1ONZ-@F_+Zb8SnVNaVhn?Bx@#wV07B+sFX22ce9?&=U&EmwX`(Cm1 zeq9#y`91%Xd2iM{YJ1JdovTE%Q(Adg|QnH#PH9-i5R4H~w49!&LS^AVgrT>PD|K zF_-c-nt1BpJZ#ZBJ$q~4^Oe;tk&7!nJic*Rv+<>^(ZRIMdo2xC+n(c_;J4%0`d62& zr>Zb_?wat~X(`uhxhtxR`n7M*2%77s`&453{1??VeGIlo@Aclfc>J_@kK0z=6&JIn zTJReP2Vb08xO!sa6k#^!boX!*?xiPARXLd+>a|=rbMN7T1m@G5Tb3+c8?=W%mGK2r z>@BOuCSFZ_42SM(^nCrrw(3uuIcB(-U};epni>#M4ES5}9X8;({g72er{*OtogHH1-c3 z(Q|whx3b20{J17!Bkh~gH1Bwa?2gGNUogK9ir!fIg7K|Ds7mZ+p5%>dcNN$svX~yN z5`Fg7Ah~mr`}|Pv*Nm*fKQ8^Of0y^Ztd=q1r~$Yqf;tdwf~C4QG&LmbJ=6ZvyoU{V zoZruC;%2#Uev^%V*Mjzv|Jka`S$Sp{oK(Ll);zJt*(c%6jO2%^A^vOaRFt>x^0X9K z8DP%hpW(w}JZFjbgQ+j~rP^$-uv~kEb?$@{cO!F6TqMuhv@Kr#M%3?@e(~fLQzcXR zPOJ&O>v!T*ljscbD@FIu?^s*3P*`r8_Tfd=M>~pUOJ@G~`+kXeZ2X-HgR5Ag4@={L z81F$FrzQsMlib=IrcLa0>QWT(tt{o3(iv9&X{CfyHVp zwXUHV5h=%Yf~63%AqPwG-X?XAn5OS*PH#Q<>;FpjYwn9)GMUKi67xM(C6ZzHa--YA zT^F)n=y*+XIVd(sHeh*jhqZ=>k4N$(k8N_z%CjOi$Ih4;qP02b;g-y!hxXr$x_ZK; zx1je==S#MbKmM;`rhM>iUO&n3mqf@O>*gNMA91dCq72{ub1~Q``HeH*RgJZ!bK}aJ z`_3n{o%zmn-QxIXUY{oO*H}D?rQ$X=CZc_z8{}PdRDtJqF<0yY;~(r#Y+jb^s@VH~ z+oZ{^ZhQ$}44<}jdeuZKY+ros$oAed4y_N@uRhay-sAQOtB%tXx_3;{ZLN0Ed183P z=19}~)gR^Ley%xlax?oe{hQ_d+TX6Uq$)l>DtRkW^mwA^lZXwaimR$Cf|nd#sdD3S z_kX*i#kwrIHEtIg;-Ac4-}m6>B(cozGjcDltJ>gWy=ut@nH>M(IJNkw^qp36=h;tw zTX#b+Xg8Bc>rUfy#Sb+uhq-MLD>L)Ripk0E`y1hPp*1hYtxI{r{FO>J3znQbqsH~9 ze~w&{7IWgOS?fxQq(cjr&pTr}yL-E_XWHw19vf#Ks*JVR{EsI%ZEL0a`JzQvR&u=G znC^Yyg5|n-d#6Qal*|_1v!vzxF+YF5ec{Hh6)i_BGRr2Njj|&?Y{JYU( zzTZmgWpq?z@+CXzw^NSk7`?2D_)_xu+VN&?llP1MJip2#WRluD=@|RkTb6B$W(I~; zYZAL6Iv)S-S^xa`&p*uZ3DF%`!VpW-&ybitz3&81 zK4(Q9XV6UQiWcJo&u#Xv+LiHs|5|7E(#Ahe6bfu?E)=Thm887r>C>Jq^Z3AKh2%#U zE&iX}VRyvP@$Mqsi0Ng=Z=MkaeM2&GJy-*-SkDYpM-*yqT} zU(Rp0zT3ZROIp0`q63|8IF4>$3~%_m>v*I0p`US=pG?pAo}IcMdx>KS+^?N+{g5`DVCO-g(VR!8{eIR4F)`~ZCl+B^n2{#KOWff zH~LMB$uz(Df~VNCpD;E(?A2HNu}ELCWh*zo)^CrJ8!o)*qAJ3N*Xw*(HAghJSXKCD zq|f5bj;Ft@eVgAbx6A%+p9~ik2V!e`nGn(Tvh6>}ci4c#`Tb9>{|-xTXfCYrU!K+e z?*Dpa@7>&0Ovyd17cNMznsvA>VfN#rmsCTte~27)P&Gd>Gl6gEl1sAg6RVOeBx2;Y zNcTP3_~Mt~?n!C27mhjYQq5?nUK5;oXIY`}5m{5#SDLTpEZ!rqbNMR=jDTB_FdQ&ztX}{~T0$^eg-q zX`KDH|7_32Fu8*43#pj(0Ng9$mj%Qc8 z3XA2QS6^bfKdxK)-t@P3PXsSLHcg_DjWNtZ=K724AEw&+t6eM+HM+9e^t1%0u&a{I z&%R|>gF{B3`(>`&?#dB1%2e{W5~oOXf_i%eQX43jRh$n#sNTf z7%M=hk1>pf=toSPVjU#_IS~J}F&EObu@R_w5QKNymnYEfo>ih_xSf__zMQNDtHeqJh*hVgWXr%LZf)w=K z3>Cnw1>~9qK1$|feJw*D>j-WM4$%zVvpfX(F(Fmt9Lj`?=GGm;| z4D>*CFT^~Mk*Rs$8`cMy7%hIOw?a-LR|3R4{@Br@osZvJttNd8Ne)#vtb)hacE#m{TAjM`*>PnVzYF zE{K3(#Jq{2u`%I^liUg5hOKM${3h<2lx_xR>(q6Q!mhJ^Zx?oE5L~`-&)?^+cV^$P zeVMFax2yX``y~E8+qC(`oRQ5RCI}tve11eTbD8zjG~UIrOJ^)$%c|v?b8>w~rd57n zc7^c~|C^ZqZd{e_Wv7{g; zza%F!NukVG&r;7wMMYGI z(bbuQ)&YW)A(>}x0Ls)LLAYK60|PTtG`$7}#-O?aMV+Ckg_!|{IwJ!MG%-U{(Aq4J zR%Ck(O)=eP0&3lY6vEwNXbxIE2NFW)H8eK{U5o}2M5r^fG)E6BLkm-LEN-ztceA0H z0jNeqGtUUaeTHUc7*xGdIHs7fVY__Zb+0>T^{08GzOjf`kxZZ)9MKVTX}{xdD2Z8W~ua z8=?8l$j}fYZ5SCEnW2Y)ks)YZDw@59=9cJjX=G#os&7CF;pxE0$Pm+gM#dQFz{tql z0zIsZj4aGC#EcCr4AK2zY+`AGAqHB93UUfkSeanvBO?|C5c5P;9|$f P+|s~=OI6j?-;E0ZTVg54 literal 0 HcmV?d00001 diff --git a/paper/paper.tex b/paper/paper.tex index 2ff2c21..c60cb88 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -145,11 +145,11 @@ are both located on the positive $x$-Axis. We can rotate it so its first port al minimize the loop area of the inductor's connections, inductors are usually designed with both ports close to one another, so we can also assume its second port aligns with the $x$-Axis. -The trace trajectory of a standard planar spiral inductor can be parameterized in polar coordinates $r, \phi$ based on -an Archimedean spiral: \todo{For the lulz, cite Archimedes here} +The trace trajectory of a standard planar spiral inductor can be parameterized in polar coordinates $r, \varphi$ based +on an Archimedean spiral: \todo{For the lulz, cite Archimedes here} \begin{equation} - r = a\cdot\phi + r = a\cdot\varphi \label{eqn_arch_spi_basic} \end{equation} @@ -160,7 +160,7 @@ radius. To make handling of this easier, we introduce a variable $r' \in \left[0 normalized to the spiral's width. Let $n$ be the turn count of our inductor. The resulting parametrization is: \begin{align} - \phi &= 2\pi n t\\ + \varphi &= 2\pi n t\\ r' &= 1 - t \\ r &= r_1 + r' \left(r_2 - r_1\right) \label{eqn_simple_spiral_ind} @@ -178,7 +178,7 @@ traces on the PCB's bottom layer as follows. Figure\ \ref{fig_twolayer_spiral} s spiral inductor. \begin{align} - \phi &= 2\pi n t\\ + \varphi &= 2\pi n t\\ r' &= 1 - 2 t \\ r &= r_1 + \left|r'\right| \left(r_2 - r_1\right) \label{eqn_twolayer_spiral} @@ -224,15 +224,40 @@ values of $n$ and $k$. \label{fig_nk_interleave_illust} \end{figure} +Figure\ \ref{fig_nk_chinese_remainder_illust} illustrates how we arrive at the coprimality requirement. If we plot the +spiral in polar coordinates on a cartesian plot we observe that for a $n$-turn coil with $k$ trace pairs, the trace +crosses the $\varphi$ axis once for each trace pair, wrapping around $r$. Likewise, it crosses the $r$ axis once for +each turn of the inductor, wrapping around $\varphi$. Based on this, we can re-label the angular axis in steps from $0$ +to $k$, and re-label the radial axis in steps from $0$ to $n$. Labelling the new angular axis $i$ and the new radial +axis $j$, in the resulting integer lattice, the trace has slope $1$. We can state the trace's trajectory as a function +of a curve parameter $t \in [0, nk]$ as $f(t) = (i, j) = (t \mod n, t \mod k)$. To produce a valid inductor, the trace +must not intersect anywhere. Thus, the system of congruences + +\begin{align} + t &\equiv i \mod n + t &\equiv j \mod k +\end{align} + +must have a unique solution $t \in [0, nk]$ for all $(i, j)$. This statement corresponds exactly to the Chinese +Remainder Theorem, which states that this solution is unique when $k$ and $n$ are coprime. + +\begin{figure} + \begin{center} + \includegraphics[width=0.7\linewidth]{figures/nk_chinese_remainder_illust.pdf} + \end{center} + \caption{TODO} + \label{fig_nk_chinese_remainder_illust} +\end{figure} \subsubsection{Ohmic Resistance} -The arc length $l$ of a spiral can be calculated from its turn count $n$ and the average of its inner and outer diameters -$\frac{r_1 + r_2}{2}$ as $l = n\pi\frac{r_1 + r_2}{2}$. Since going from a standard inductor to a twisted inductor does -not change its turn count or dimensions, the combined arc length of all trace pairs of the twisted inductor does not -change. Twisted inductors require two additional vias per trace pair, which will increase DC resistance slightly, but -the contribution of these vias will remain small in practical applications since the overall number of vias is still no -more than a couple per turn, and since each via only bridges the short distance between the inductor's layers. +The arc length $l$ of a spiral can be calculated from its turn count $n$ and the average of its inner and outer diameter +$\frac{2 r_1 + 2 r_2}{2}=r_1+r_2$ as $l = n\pi\left(r_1 + r_2\right)$. Since going from a standard inductor to a twisted +inductor does not change its turn count or dimensions, the combined arc length of all trace pairs of the twisted +inductor does not change. Twisted inductors require two additional vias per trace pair, which will increase DC +resistance slightly, but the contribution of these vias will remain small in practical applications since the overall +number of vias is still no more than a couple per turn, and since each via only bridges the short distance between the +inductor's layers. As a general expression, for a standard or twisted inductor with turn count $n$ and twist count $k$ ($k=0$ for a single-layer spiral inductor, and $k=1$ for a standard two-layer spiral inductor), given via resistance $R_\text{via}$ @@ -244,14 +269,46 @@ we derive a first order approximation of the inductor's DC resistance as follows \subsubsection{Inductance} +Even for geometrically simple inductors, analytically calculating their inductance is a surprisingly hard problem whose +complexity quickly escalates with the inductor's geometric complexity, with realistic wire shapes as opposed to +approximations assuming an infinitely thin wire, or when taking into account differing magnetic permeabilities of +air or dielectrics and core materials. Instead, a number of approximations are commonly used. A commonly referenced +approximation for the inductance of planar spiral inductors is given by \textcite{mohanSimpleAccurateExpressions1999}, +whose current-sheet approximation for circular planar spiral inductors we will use here to estimate our inductor's +inductance. The current-sheet approximation from \textcite{mohanSimpleAccurateExpressions1999} reads: + +\begin{equation} + \label{eqn_mohan_approx} + L = \frac{\mu n^2 d_\text{avg} c_1}{2}\left(\ln\left(c_2/\rho\right)+c_3\rho+c_4\rho^2\right) +\end{equation} + +In this equation, $c_{1-4}$ denote four empirically determined coeficcients that together describe the coil's shape. The +values for circular coils are $c_{1-4}=(1.00, 2.46, 0.00, 0.20)$. $\mu$ is the magnetic permeability of air (for an +air-core inductor), $n$ is the number of turns, $d_\text{avg}$ is the \emph{average} turn radius, i.e. $d_\text{avg} = +2\frac{r_1 + r_2}{2} = r_1 + r_2$. $\rho = \frac{r_2-r_1}{r_2+r_1}$ is the planar spiral inductor's \emph{fill ratio}. +The fill ratio encodes the fact that the inductor's turns have less flux linkage the closer to the inductor's center we +get. While turns close to the outside have good flux linkage due to their inner area overlapping well with that of other +turns, turns close to the center not only have a loop area that is only a fraction of that of turns further outwards, +the closer we get to the center, the larger is also the fraction of the field lines returning on the outside of the +inner turn that pass through the inner part of turns further outwards, flipping the sign and contributing +\emph{negative} mutual inductance. + +As Equation\ \ref{eqn_mohan_approx} approximates the inductor's whole set of windings as a single, uniform current +sheet, the turn count only appears as a single factor of $n^2$ in the equation, with $\rho$ and $c_{1-4}$ correcting for +the inductor's geometry. + \subsection{CAD Integration} \section{FEM Simulation} -To validate our analytical approximations, we performed a series of FEM simulations in both Elmer FEM and Simulia CST. -For a number of inductor layouts, we performed simulations to determine ohmic resistance, inductance, and parasitic -capacitance. For a subset of these layout variants we additionally performed simulations to determine the coupling -factor between a pair of identical inductors at a number of different distances and rotations. +To validate our analytical approximations, we performed a series of FEM simulations in Elmer FEM. For a number of +inductor layouts, we performed simulations to determine ohmic resistance and inductance. Due to limitations in our +gmsh/Elmer toolchain, we were unable to run simulations for parasitic capacitance and self-resonance, or for coupling +behavior of coil pairs. We found that for these cases which require larger, more complex meshes, gmsh would frequently +crash during meshing, and where we were able to produce meshes, Elmer would only converge for some of them. While these +are problems that can be solved through either a more skillful description of the problem in gmsh and Elmer, or by using +more robust software such as Simulia CST, we decided to instead experimentally measure these quantities instead +(Section\ \ref{sec_experiments}). \paragraph{Ohmic Resistance} Determining ohmic resistance by FEM is reasonably easy. In Elmer FEM, we can use the built-in joint static current and @@ -274,6 +331,7 @@ Determining parasitic capacitance is more complex. \subsection{Coupling} \section{Experimental Validation} +\label{sec_experiments} To experimentally validate our design with real-world inductors, we produced test coupons with a number of variations of twisted inductors with winding count $n$ between $1$ and $25$, and twist count ranging from $k=0$ (simple single-sided