From 812dbd651411632320cf94da2e46171dff9f1b45 Mon Sep 17 00:00:00 2001 From: sjplimp Date: Fri, 9 May 2014 16:16:18 +0000 Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@11959 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Eqs/compute_fep_bar.jpg | Bin 0 -> 18106 bytes doc/Eqs/compute_fep_bar.tex | 7 +++++++ doc/Eqs/compute_fep_fdti.jpg | Bin 0 -> 15544 bytes doc/Eqs/compute_fep_fdti.tex | 10 ++++++++++ doc/Eqs/compute_fep_fep.jpg | Bin 0 -> 18055 bytes doc/Eqs/compute_fep_fep.tex | 9 +++++++++ doc/Eqs/compute_fep_lambda.jpg | Bin 0 -> 10511 bytes doc/Eqs/compute_fep_lambda.tex | 10 ++++++++++ doc/Eqs/compute_fep_ti.jpg | Bin 0 -> 18149 bytes doc/Eqs/compute_fep_ti.tex | 10 ++++++++++ doc/Eqs/compute_fep_u.jpg | Bin 0 -> 9337 bytes doc/Eqs/compute_fep_u.tex | 7 +++++++ doc/Eqs/compute_fep_vol.jpg | Bin 0 -> 15209 bytes doc/Eqs/compute_fep_vol.tex | 9 +++++++++ doc/Eqs/pair_coul_soft.jpg | Bin 0 -> 11309 bytes doc/Eqs/pair_coul_soft.tex | 10 ++++++++++ doc/Eqs/pair_lj_soft.jpg | Bin 0 -> 17984 bytes doc/Eqs/pair_lj_soft.tex | 15 +++++++++++++++ 18 files changed, 87 insertions(+) create mode 100644 doc/Eqs/compute_fep_bar.jpg create mode 100644 doc/Eqs/compute_fep_bar.tex create mode 100644 doc/Eqs/compute_fep_fdti.jpg create mode 100644 doc/Eqs/compute_fep_fdti.tex create mode 100644 doc/Eqs/compute_fep_fep.jpg create mode 100644 doc/Eqs/compute_fep_fep.tex create mode 100644 doc/Eqs/compute_fep_lambda.jpg create mode 100644 doc/Eqs/compute_fep_lambda.tex create mode 100644 doc/Eqs/compute_fep_ti.jpg create mode 100644 doc/Eqs/compute_fep_ti.tex create mode 100644 doc/Eqs/compute_fep_u.jpg create mode 100644 doc/Eqs/compute_fep_u.tex create mode 100644 doc/Eqs/compute_fep_vol.jpg create mode 100644 doc/Eqs/compute_fep_vol.tex create mode 100644 doc/Eqs/pair_coul_soft.jpg create mode 100644 doc/Eqs/pair_coul_soft.tex create mode 100644 doc/Eqs/pair_lj_soft.jpg create mode 100644 doc/Eqs/pair_lj_soft.tex diff --git a/doc/Eqs/compute_fep_bar.jpg b/doc/Eqs/compute_fep_bar.jpg new file mode 100644 index 0000000000000000000000000000000000000000..772ec9c0450a35c52b5b927cbf20e7d77e373c93 GIT binary patch literal 18106 zcmbum2V7H2w?4c>uTljCAu0+gy@LXg-U+=59BL9m5;_3_Q4|mmQ8|EuiWNkfQk53z zDk=&J5~L&?MUX%u5~B&>+rIC;?|Hv_?*0GIcfaAclP9xh_Fl7QX3ewK4BPLw7XV2o zJ4ZVJ0)YSy;2*F}74vtrwhndogxfi~*n&3zK+M4fg~jnm0ssb^l;CM^wbwr&aIfGi zfCmr;1OQzC2#ZLJbM>LfFR!W3nTuCHU3fNpZNGM9Erh3 zf@OZm92bd+{DlWWd^ROH3dFoFAkIxeMWurHEr<`qCSy<_W`S516BU*S0DNM<@{^(> zkRa9pu~>q)r!|Pp06<6#@ozZ%-*8eC9+VRRtZ{K^2`B_IY44$k!+Uj2O-=SXM5V?? zB_(OPhee>n5+e6n<1ley*faq6XPbZ30;GTGb}y)8BVAJ?BTYRmQ2qZ(|HqsED)oN` zzxwu{B{n?%(Pt337k}pcS@+L8+${hw*#vcS;m^GAD*(`u0|2|of94&y0RR$b0HA&B z-`XShYrG(nlH!hPYp15BYN4Vcw0|PZ1f9m1?Wwn2k;TQbpxCVjD9WEdnss%`n$pXBz7XY7(D8PH-I(P^2uYPk8_62^; zJU{5tKgT_Y!TbOC{C|D$6oWr`5>be~zp|}8z4t~WC#3ws;GFpN!4HT45`ZkQ8&C#R zfJ1;Lpa&QO$AII2E#L&e0dF7x2mvAhB!B@DfK-40oC0!zLf`^W3RD19z#X6#Xat&p z4xk(81BQW7;5G0Lm;n}mkH8mz4ln^WXvhR1;t(0gZU_`|5TXvzgP1@pAhr+}h$kcf z@*4yJ!9tQD1juPfA>%ELnx4C$XCcu9$p?X9$6kG9#tM~ z9upo*9%mkJo?spXPdraL&l#TcJePTH@znFQ^YrnI^1S0&;Q7L{$qVp`^2+h<A7=a9da{|`{ngpH*yb)Lw*c22L+%2dsXf6mB3=>Qe%oV&MST9Ht z92fj3$PyA2f(q#g*$D*-VTH1V%7pF<^$Lv(EeWxOC4~=zdXCQ4dj+=th)Ihb z5wjLMA(kw5UaUs!iP*H*hPb%6s`zp7K=CB;^WwGQ1LAYytQ|5tw01b|h}=QkQMsdi z$M}vl31NwY5|$Dn66q3U5-k#A604HJlB$x{l3|irl9iH=C8s1erDUXZrQlK+sdG~I zrJhNBmKKy&m9~|Rls+SUTY5lxQHEDWMaEhtLguv09ho7SkFo-?YO;>9F|viS4YIFf z={u!&8tnAliQiedvuEdm9Iu?JoTFTn6pko(D5NS}R~S-QRg_gcrWm1EpxCTP-ovx! z$R5u<8GCN;d9i0xNmmxiz438j>R2~^q=TSFON2y;^f1|;#VXA@ExTP_rDW++unW9;zNzszia?#4x z>d;!#KA;__eNlTvo2z4}6RUGaXGT|A*GV^9w^R44-VwbBy-K~e`r`U_`b7Ol`V0eg zgD8XR2Ja1J3|$TL4EqhYjEs#Ej2exWjSm?AW_;Cn%0$-0-Q=9fQ&WCZD^sFrx9N|g zMn{v5HXmI-rg;o~?EbOOW@=_pW_QdM&G(y!ncp;Du-I$yo5c-_1=v1V80;2|dR*mr zOOUrPGzi)ycKQ^@H0% zH>_I+9DqB*OW?EaYVPswT^<4+?jDsMpFDLv37#WfGG3ux_q~|jR^G+lGd_oWl70Gp zC45i#*7|<;v+=v+x8SespXomupb&rxcoZlY=o?raxEW*{R2ua0gyD(Y6O+Me!T8{3 zAqpX}Aw8iIp<$sdzw!U(_uKv7IAQRxTVb2wj^S6s=@Hfu#Hb`YnG z!{gq>smJBUEyN#roq2!!oN{U5FWeO|RH?;*Xg~#Gw zq#a4iPg_d2OTU}Jml2WCPuNE|MWAF_X5P$#WQAw-6IF<3h#ybdpS*WUMcBoAm!vMGUs^12EouLK@9zb_e=7|weO6{r zR#h%io?O0g+2!)1D+jJzxWcJGR=lgUs%*Nt=W71d@7E%)jbA^0y|GHEs<7(k4b+YI zH|=k>-%`C*c3a?f%I!~geD93hHMv_`tx#Q9y;Xy)S-9tUZ?M+5w)Xy>`^9xUb;)(h z^(X3IH`p{hYSe7J*(BFg_yBm2{9xtbZx1J%otyhxOj;US54K)ylW8kxhqR})(>stI z3y%UGy?N~PxWDsQXIqz6S55c6?#iB>J;l8uy=Qv2N$I4`Cvi_!`w)GL{h|Fc1O5YV z2R#N~4LJ`z9kv@D7_l57JvD#Y{p{$o$InfkcZ?d1w!biZ(e~2tW!o#GSM6iQV~<{& zzV3Wu_NI3nHr_X3Gco+u@$Kk4w|8$QeJ0;eotRp9ANl_CbnG;PoI+;LoczH5py@CD zk6+@xuvc?wQnagUht^uxkFUR=`_n%%5*XWG&u#49sQG5_t$)*fbB>8&vcDIwcC+sN zF!?d^)9>dJJC!5Ixx96FtCQ=@{jiPM-rlANsM_LD(E#A;3LF91fDj-65de5W1OYt> z03!V#7-SX@1&}NJlVkWo6#s=oAcy`epNIMfsrbc1z-Rs=f&R-sc*#G%`7Y%Gf*|S0 z26M08fc*LN8$AD6lgH);?|)*DjeyD0%i7WL*SDpmoi8>fEXLQs_4HGs-7xwwa2+fCcvB-27cVEzc%wL@bdPkyctbBo zb!THkS2uW^ZM3V2w}_spZBm4(kwdtbUXqEay_+6N2dQW5h_g*M@{5he*(c~}M>`sr z>Y1je`>E^4M5lU1!QHX3X~u9&T%dY@pGbP5kC#zEnx|WYtGcV6NkEuxqN$#7cuH8T ziDP_9aze6;t9p8bHQd!C!qnc^Db*z=+SxloCn>=@B`h+*IY}hl)lDzaNiPxW@0Y6Y zm+G!(l5FIHjnpwtGD=U+s_0H-i@U!=36ZJf2AUy_w0);7_{ z)m7ii)5R|^HBH1c%quw{BF-D@YaAYJViRMd?dgC}$2rD@2Slaox}!WDo#WFmI_dcE zu=Mb-R9z>mNtBxp%F70Y^^9}W(-jH8SjXDiSsBH8Aq=tl?xrX`<7kHf1G`uogIEW5 z_jLD|IC~q%xEO6L+{)I=H{Qqytz+zK3lFq)@{Q8N#EOI=)3K=$Q9f3w?)u55)Tk5(FUPd7^jICFgCE=~$p@dN=beBsHH<;(XuEo+rlloDT8Ut-{Y`M{ zxD?wsL;Z-PbW7)e2;D@#@RSIfCUlEKoJR;J^ADieGf$=hQ^~SnI;QhT4(_^A^tRqvyuwHr**Z{0cy1Tyz);Tsk zTGtq@XP|3mW8jN{8^p&ah!`eV*{j=N!o1XzebTI*66{lTEUgUmU1QY)u!iwCd_ug9 zXEe$kp>UcQX$2U1P z!3`gaOGwu9jrBCe+PQn6W5e9Arf%^GF;P*v5k3)-fq3gAw1G&B2_A*PhO4{lM(XKf zOp{%G)V&cpNp|`X>3DBjaCpbNq4i@yk2=!IItGPs(vJ#=ut)eN2e|6{srwrEins*m z8=8b!n|N5I_yxup>l!#93>@q{vEDd+=hOsbw1J0uYErC^yH{Aav#(FMu8X~Wq<)-z zf)O$?+A~4jNCfYR^@`O=aS062w~w;HI--$L@#)?v5&r3R1}G>~CV@ zYhr1tZS5A0uu3tpwAXjEH%_$1`dC}*TF0AO#zk5tS{Z~{raD@s`b8t7)kSRG4Sd{i ze%iLy*0x5mw&`K$2xlX-y=lCqNu&qP9cN_~XXBHGvbKx0jR^F$gu??+$XHX`1S30L z9V>r5E0KhFhXf;sWE~XN(9+$=KHSJIN(bR*6r*oy8EN93f=^CBBx|E$qU;<@{K5^; z;RYCed_n>uP8+4~>xK385<#1KAR~QZql^NOIw`J>9=7rE5%6g1XeYG3wq<%kV3ND5 zxybemVEro|^&g3c2g1X{$MY-k@$&NW@$(Dt|4IS^LW1B0{ty%q6cYZG1O!DyMTA9v z{rL3|u--pvffa=X_yzt^jygI5s^{R z2qY>dF)2AE6`z)V`bpxyu$dp@okg&o%Q4AuXcee~m zT|9hzynKSc+6CcB{nca_6j?I# z2nw_yYhMgki(#B=rWr=ravn79{raH{DQPuL$5S7j=; zQg84S9Qq$GiB~vs1T$}|I!iKZYW_j_08R{_@nngKVU;chH3@wAne*}8H?At%3K`hg zB-xP@ah@z>jf!bdAJr#aX|<`!BH5uCIIf5*>8I)$0I46i<*m0^?V{|c8 zZXOR^7%L#SM%19nl@+I2&s=M)k3E=cA5`}xlS%LTa73ExtJ}pib|dBaP1GA6i@Juv z-gG`Y{%O)V&Fawy-jTh2c1yp{(}4{r;kx#gRq=Xx|cRtn;FL{ zrWV0HSr~?Oe+p5ayVLQW!&l2Nqiag-`BZb&**V|oJvPXS0;{v9v+7c|0pnNp%XhOp zwt>EYBu(olFhPr5+&S)!H`mvxYOC+4t*kl?qcY}LavG(NuifHEv;F19*`EjBah~#O zeJOMfU7K2Fo@zpJkGyV$%dirCJ4p1k+bE^Y9NL{x4SC7uHy1A%hwR?%FFA0}0McVC z>ka`g!9f_^eH$RdhC-W3tEU)+)Q$o3eTJ~}i9wbWTyE##qJs)m`J1T42?OUuMMvdt z8SFaDVmj6EVlz)k2!jnH7))7+bA(yC^x`3yWE)W)Upb&G_khm5OYKQt3o3FBc+}qR z5Y_#t%np%OorDUwlK)|;g0seIZx3zj;OsoM;P-?zcZ`%X-x8f`VZiF&uc@`SWGHaZ zI31pgxnnnb#JuOym#HO)&R5hc;g?xmuYZaCKV5=L#xz~FHFp9g1VgXCccygYnwc*o zvW+-SjE1Sx$y-)mSAG&@GH)7a`uUv=>VG(b;oH~R=3Dyl%KQuRemE)gwjrxy8{k)E zy+bd6ddc7lx0aCvxSFhrnJ4pdQH-WST(<-rF=V0oaH4gzSo{mw%5BQmNP0k};oW90 z8y~#3Q<$i}YnH886FN}0JgIQ4`Bi&|``tlQBKlzW%@bJ2;sy2FiO)^MdV~Z{8h*Z2 z037-sF3u%NZb3M((U|=4MVvE zyRII4e!qdM?LHezl1~@0a!KXeIO)(fuu$JAcXI)Hx=M_QBMKtNQW-ML7)Bt$r%cf~ z1JT({U&s!E?hH_Q;fLLlUg1VU%9DrgHho8bV;`StCGJE9s^xP`>w@N4sUEH8fA%xS zqsm0jM!7SdDK?3ns}~A;s{qX1DmcXZwVW#~csFKFZ>ua>Vn%(qv6Fj-b)z-FgZ} zk!83Jy_}e_mUZolDto-6Bi4BTYKM`^wRb;HFA8%a&=gF{(i4S{%FIQZ_LTAZ&B7nC z_0?6-{V&bpTo^aagToVGok-p#I4eeCH}TCC&WUZ{iL2l?P}WKuaL12w&y7)+xI9Q0 zr>#+xEBuVH4J^WGnry>ag5}oDq-{Vfh!8x%AyUWqSLm#x$6DWfM|N&8FBRdKW%@fK zn|ZLY%U;m~i%cd$lq zl%?^ocjS-6mOnb#);5^6yX`QGce5osvOa$a#tp#>NupUocy$j}AtR3}P(rEVA&<(+ ztW?Z?4V=l3z8Ic+5TQb7c3M`jd7PT+?d}XYuB^Tdh+8gd|I~*SRi~rL2 zw$cXBGFfi}zkw~p9~~G0ySX`QH;dSBeDvK??)dk?>jo3wPF9qb&A0n^ei&7>PZjvK zf%zaD{=xXxr*^YUc5>DbRMgCwaSSxn(nNGqZo0%df>g~w9e%|AU3X%2;QZ&5mS-3- znYo#63T-hBx9Xv6>;5vC=X{jw6R~X|_XeYUYj@Sq7>DmQ@dw(TV<>oz^!Wu>i@2bA zdK(xG?4nmPXSdGxnz1S!=&5~hatUP{C?vpZ16*rSz9C8sOcAFur(3g`8WeiOj%{VL z4IC&^rYI7cS{WhwY+qDodBHY-)@G@VoWhzVQhT)f6IrK&rkYmG^r3hFx6pMyr5$apIXBB8k@hEQfz7JFXzVY;rAdjko1r*NZ0(?xu;HxgiQ&|gsuobI z4gQ2fuUlQUJtEsD+kR+Zl9do1y*`#p2k(cFQOwuthxfc$@jTkq_PFE6ZLTnsVa#mV zx?N0jWn?VkXoijW+Y3v%Tn&6BC3V2rvD=*T#lLM<-Kq2Z8^h7c!ec_$oy#BPem&?< zsEpgWA$slHNhslO3_E-WM?^>`aNSs}3vXrdQfovB0`f+5HiwO*8%4yAmj88$4>H+SS@$t=TU387I4%DP0b zBjWyt71dW$*3S8{3dn}WhSeXX%u+@ZN0zu)Ru#c^TB&0n zV5#^26klW=g^GX1$^PWtRKC%Xo;bf%NsI5pp>~wqOUvl~RPG6%KkK);3ZaqyDjo7K zZ4Eu)@%N^AX8eiNA`XHA&FvLqqz;CjRX))2rd#v|Dpg^!qi#i>M>I(B7@mw;s<5M| zIJ}v?OyB7W5J2nmH|FjSFE#`mXUB=?txzV1Rm#@Nnok!m&NEm)r!1MbSiCx0O+*+~ zCD$Mc1M!rXj(5EgQ<^uN(Os2E8|U1nnm+xoaMGS8w#(=40}U`1$~v$O6xW+sQq?m< zwgKw(hm^V*A%b6Rbzx$RnGCh?;iqM*#Z_&cibL;Dw5lcxNjk`UydiOG8=%}Xi`oY4 z5RAla0Ac{;2EO^L{JoEw`l_aRxgw4XFXm;?-nVj4EKxID6kBx##)Iiq;p{!tK^UYc^Xt~x^f4VoJ9?tEKm43DK9UkX%66Q?$JMZc)WFBTL6?bbgw3(G#XS3At zw|y9bXSq9rmpe&k%sd*p;P+yQ@R!?mSx_5x+%Xs*4AmqZOt62;J;chOj1;y7V>Q)1 zyBQ%lHK>*t<-NUct9#okaOU*}88!M(7^G{7Wf6~^*svlJ$~=)dGM**FB65Yx*&cX3 z_VF&pRVEk4x<>gD1mCsXsa#nzliyfRi7a2e?e+Njx=X=>Z#Y;P#^S}`g~p_Nbhp;?odJOe5v9ki#FC4+l=GA z)dfS56o`GEH(5k>LU3`;HXvXYZ#`?%3}P%T(B)p z)^~XJgGx60vd+&D=8-oRYAku?tF60c5)6H+eZC=4YK|k$!Yvj{Eq68*8U}kgv@qmu zW>QBpLoiz7Uq3}oU_Kqqe84t*P_WZK93nslwmjb^vCTt<*)DHa7avb(?L%r|mWo15 zFXm3#c?}%qKP5oY2I*6YKKeQ@>mcJa(_pIUk6v(!r?N`!5%#_@^zC*YYy0eBiMfv_ z7~DJCo7`J;f4SXD)wq7L8LM`zc$(OjN>f}QPKz>8EE*fmaS)pmr9*R?2=EMyEW_4t zewwOP_Mr7#?UD;+Uy*;&*naJF`ZmB)9a;SdYIM4WY0XNb6c_RwCL)P4ALa=5th!8D zNi{M7-tfV(cBQ-jX7Ij8kI=} zxxjq|lNf|uM-Tqu*=TQ+M|-w+q=XZ|`9NQyjj>&0dR1O0HQ4uuHYdEFU6CZeAmeC> z_d-JWQhY321pAhk95)CT*Ij9CsalDl_43A26rk2e;%Rb5ZZC*?YA*EElz*{HKhjuLL}&$(4tJoDqDjTj_B@WvrR4Kd16)~#AV*6gr|f>& z1vSq8>xaRBL>>P%m+4zCQ>pX$$MwY!I`&@rW z)GYmdV)2iFn)AZf4bn3z~dr@3=<;cYHX!zRYQ69<6&|)nzrb2g&;f@&8Uq8oz@Bb4G%; zlkV3yzl+8(`{{DD>qHZiP#%gz7WKSsA6X)IHHVGODxn)#wTx5>u1|tL1}2rI!#O@q z&|e4&2+z*+3hH$Ziq{y|a38Gy16Sr4tm06vwYE|q{M#YkA>v=`*?(j5o7+gNL&Q}m zrC87(&mInKhY!FcSawT+-E?vYt7Nz$>w=7D^9*xTKIlpWa&2MmI;QKCMo{jz6O$vw zBy7|B+Z058mKq*Lh0~JhW0s8KYy(y@ZrA6Z9p{rqgSK`|rfJ^H&X`HPYTk|0+$vCc zdVhE04UZSKk04clXA$?ylF6DOJ)9b;l0hl&U>#s)2&IAR9v_RYIdY!hcbDZxltia*Zsp|? z0`7f|kMTk=dC>mry(0#$$uZ6C%=QbddJ7t7zm)D(2KnLNSl|~)ycR0>F=p9TGZFNz zWXbqfYZFW&%dk!&M?o(C?utekd6IOnsPT6Fit+P%W`DFf&$wEUl|HIem^<0~rF0l= z0|vxC6|O3GlGqx*Rokmgz-(2wjmZ-B(C3GWWe8d<6v{ZS+Z-*|br@{( zd6w{9a?Yksq6Ev+8cO= zxRwCls^{(n$r6$f##ZN8fJ*2&#`L8(^=GP4iwjrlIUv8T)z}QWW;0FxjEdJh?Ygt= zT|?=+4-G2L@$6yAQJx*vWg!cYS~Q`w5IfkQ>#MX zs=Sq3cgxrYS~43=G->tr@geT;3UZS;~IgiVPsF&VQyt_)J>zcHNFszkaIp@ZwWp*wmH^wqRo zwb=K%!EmrO&20D-Hq5b96tjDVwEM|&V3skX>P(gbOMhryDr+zP(wH4x>(t#3=)k$A zdnbf6V`FKHsG932#WO`J_9+ohd<-BPBY%hTe1xxp9ydQ^t7(%svqAM+eaz1MY-F)# zqE`oR1w9XINx8Chm7Fi;sYlg`_EVaTYnX{wy2nCDm4Ey=M8al~$qo~+ z7#Qo|NKxy$G%I_;ub1^Mo{}-Dh?8B>K^d1}C{UT;)hgG3p*zjO4bKDZ_$L=TXn6t2Dao*wCO;KdB))8j|pB~Qu6%{Ts{*QD!W zEH<@R4u9K$PTK}n`xsEGw$2N6E1fUf&$s(-1L{VRNRX^TwJf}`4oxFt(@WGE+BDmh zHNh1rl>lX#xwJ~qX6Y{G_wL3EdbP5mZmm>YV|LUm$9?!Bd@t~hFtarG>xw%5R=d#} zWsm%azPw4;L*IM`>m>gY$PtO%cey-$o6|Y_cj4#dr-+?%LRH zG{Qr^dv_!gPJjetSLC$$Q_eP zYRkD31wV=q7K<6grb%T?<$-q62!_y>=e~qBLkGsh2>w#eY-`r_Pa9O&P|)Warz|F@ znOLeT+~?Cyk!A6rfgqb%LLt&m4FhCu{E9#Sk;;+HUM5Db7tBAb;mD?tX&M}3`u8D0 z%GglQ6|GxsCt1gaWP+w$%?G+&ocvc9$iP!SN+NZFuf5k$+~ghR>W>p36sQzyDx~Ed z;!SIpeb3`Oo7YWkl|Q5eoCcy0vK{)*miOp(bCP&)1q(V{C1$}3Zki-A6sg{G`i$>+ zgu^wTJEsa8V|z!8Iudc1J)U#VB(A8HZ5%bI@0u4|Dmf0VB+>1w@;z6!0U-+mf(b*g zUpxQ0Gy_8#T32NC9_r4dw+vdyXK%Ppf&r?SbOQ6cJTq=cHzVWem7BgBw~n12zAD44 z8VQ~5qWTT3??Q18(-E{TMg*n(8m`7ZLN#Y0h$#H5=EPCQ14VIQq`E@s+gxJ4k78s& zWmvILLr>M0m_xjDFd`epK1lEYz4mDB>G=_G;iY@Pil)F2{o8eIXultno_hjiT)X38 z!Who1;fCUb?96Ux)bpct5Avzx%40;9dQ;z6VTkc0Y@v#{yIXV{5MHg4;L3Btln*g# zIO^siBZJBZCK?dq>q)F+XV)WNCu!P64MT5(#?^xgTXRu&I?g`55<2~8UoLrP!Q4&< zzqMOp5Z^<*KQ4hDXH||QM_{XyAY8|N0q))y4}TdWTMtgAo9PoASi!Z^GiZf|p0cWH z)w)DnHPVPgKfhe2n8f71zD`zrT;=xYQS14|Rr*U~C_QA6y8Z;mQXAv!WHaTrs=Ij? zUxqSs=y|8QQFXH%;yaE~<2De^@oTPhxIm7<)dyRJb6;n_qZuqcMCYGzj8d3!Hqh0{ z`+2QNk@cO9=p(j<_BEZY;>|i>QEdUm*Ey9qOj6%$qQ1@4(hlybkct=8INNOBsrLTK z@2R_g+~fUG%5v2%B*v~!lepp(mO0y)BhSjejsHS%ySq@8pJm7xCeb$n>Ak0Kd=9iY zr#>wSs5kew4H_OBNv4GXV%ewrJ%*ms&HzvFAOt@8WV`bziC_SBtX zePkaE<^;2@u}ukHueqA&kev+Ufu59LPu;uz%irBs+B-bXYOP}BR)n4GHP9U|&Ws!( ziWUH%!4rOrYGOsta7DuCS-WZVy=p8X^AZEI4V3F^(CsQ#W?028Rlofn)Yboz}ry$vuESyvG3Oyu0|E_!#T-#M-#dh+_7H)gK! z2foXbtM4{G!&W49T7`UYO*z=!S-M714!-rl#m0x723=iVcxlWmc}t90-w{($c7?&~ zL%$j##_%b+^K7fKiA;uT{7fqM(394Rom*j98@QagySl7>RZc?f^K*bxxK)>>j4x+e zZn7v`tJvm^!i;+b^;OU{Qe>K+(L_)= zO7W%MzUk1$(hWZvl ywN;l?EQG95)Fe12-$p9*kj@&+V0cF=zURKdVX*tU+8&j# zjhOSVE{PWUtDYStJ-^6XJ$axibHd;YM$K)!wb1WTMv(udNwu!7vX$_AkHil&>zfsy z8hsocu^|mNfc#h^hQZF$vPpDbBH2Vt;zuG2w+*}~%?zgNQ(%P_5-hkUed-($30L4a zy4dKqu3vv(7vgWBZXUz=j@i1R{Xn&IwzQ$>)RY~8f{b6f+d%0^{XMy5-?I2Ib zn~(6J=sRp1HT+t4qCAb4uFdpdR1Fa&pK=AZZd;gTy_u6C%GutXotX_rDr9w0#U=XN znGc^6z9hf>jsC7Dr+d6V>P+at!3W2h%9fbJ-A&Z>{?NR6B@Uz!^eb-Pw79u2Yvq5S z?2vY&26kV?9CD3@#jO2?Uuu7xP2GjarOG>ol^yz{=-nHCfPiAl6Ra77pt*o?WMRz2 zDKq;zG*p7CfZwp|peKLoy5~sDz#wYz8E$W*n=@)56_kk1icj8`(hinmo)%|4y)F6$ zsz{867Qp1XV+lbN=*-xn#6ZuX=@B$&tk<(KoIO8dIuT&pd2rOS=g|f<71lfb_1ux~ z%+Q=rzFsAQZ1ITtf|B0av2_`IZm0~a(EV*&#!Js_z=Kq_>xMo&F;U}E`+LoXhDFzz zeYry6MV=-X<=@}qT`bP7YTgEhU}xq`iihSjw|cU42-f4acgjG+hM%12dsbbR`KX+G zu#>-Z_}k1^E*tk^+P5hew(yVy<+#!}T(-)%V#cdr)S8;tC$Wpw(-v9~&rxEf##3v{ zZQs1nR+-Q$-L>ET-U@V@xnZm2N$oQRa;Yl3#}2 zoo|((?WQL#wqIn7F}o(gi6xQO$*F4T7*JBALJO0?pt49#cSaPm;izlYx_t-gM#?x& zqjk!$H1uUqVO`m&oLh&xh@X#=v`EON_lm)+E~@qnuM@p|I0Gim(c8M&4Ml(^Qy~a% zj%$;AFko~oBdunx@Lri>UD5vd=!SUl7je%p7#(|24H+PwME8&=>{VestS6X({#Fvl zls+}Ir8>39w++0vFk|&BjOC^etrb(ud5}tLa+*P_p3?_6=^kNw9!EZu*PDIu6hkc_ zo;Ev3p9$J3B`!Rg=QXoctz+8|oax>qp0!@#m@LhAy<$#t^7IcSF@Y&}ZTqyGVr1Rp!N?|4y6XC_t%vu9voPh#$~ljY1@_+9sw5#uVp*@U1mAUQ z-a(Vgx~Q}0pvMgOIkVu#AA)`ixrT(}*MBl@798qWE!Y)t-oT-Ow$Ra$qmnDM7)0EW z#e;XI%nwVDB^IMfH$Q$q&sAADnml|rG3)cE=VNXYl$O?shRcVdS{(Ula) z+AawedOf&4Y6I>|4LNlU)Q%`#D_0Et=1eiBSueoPfSUtc74Dm(9joz+5~5^$&CqyA zb=87IHdn2S0WEA(sSawJtI4=Ea7XoKexX+I~ua zCVnwBhlr3k4VCOQW|3bp*9W-D57D=4mQgYx^DZy;XHR}`-fzG3^4O3_+NJ%ti>aMj z{%IhGo4!9o83R|b6WsB@sUodp61akp-mGFGDh{jUS-(lTX0FmY5$0R^uAJ6!v}eQV zmigE{z2CRSThhQ&8qgsiA(Z9}O=L@_Op zp!oJ^*@<%nz$WQ5tW~vc5!@`Cm*etq>{v;2yI7+OvucivgS5MijTMcR8Pzc_({`4= zyZhSV8i`mPWAxQlL-(k2?4V$QLv;DdQBE*8oqyvHa5JYDLuol|+zFPWnZY=6PJ(4E zm^=Axz7jmtvQu=Z@1|q-{S!Ba8C()DG;hMR3P@1sOF15+~;c zxO+f7l^UPpWK!luP(QWWs9!3zAHHn(Ff(H>+tFi9O`h7&dIu7xZTmWzmf;|+F^(<5tJoYeM$V_DnkvOvO#pID3@F3Ob2)%TK zv#(sib;Y{=M9a*WI#S@^H zLLRQeMb#|l-~TYPTp`}XQR$4zoi!)5sX2#+f=lbBqa+!qfOHiL95PEZqIbxuYzvTD%%Hw1^Pj#4(%f z*1qxis9f=F(O|b%nr>^8Lb!QPw$+R^E^^||n`3V5eaAQ157}14XKSGUZbtk<0*^g> zd#k<-Jz2$PCJvshQDhP6>Xee0)0C;4q(9z#Gcha*U-Ew3(OP`=H@59Scl|~Cb_21I znEl!@3t6UFugZz?S!!9YLS?_f3InHd2(I+?;BxPCDBq)*Z;v)KybTxaQq1Yh_PjW% zK-<`-`@E{3deQ<6S!QDc(cInbAh=9`=4PO^^SRKiJKaIVk1s~eq^djHxhfNC?|11I z(ULO~re`+pJhxa|WN33_MySTcq^L30!SyG^_fRHr>nc|@fIA;(oQvgXYn3j-a><)D zc?NKq6OQIX%-ULXb5Qj)tqbKHGQs(n#=9Ah?8}iIGEzIU=Iq%=@%pY?cQ&Equ7Qf` zyVZo_?+9x0r_FpKPy8b`yPLB*cVHT-~CRn6VGL=${%Wv$hzmMs2w-Y=wTm&d3Ne@Za-L#1;qT zN#931pe1s@Q6?no+j5|CJ?cM(aN`KIeqqhujHKr8E^G{DTX(xTwQp4X~ z3OBg)*k|>QUjUBG`y%nYW>7j+Zwe34?!yS;AH79pdv_Ao-~z_%vR9Qtt>*Ws!} zz9QKo6h?J?B=W+@{@7$O^OC+f8G6%6Gd1vV5ME}$S3x`5z*)!uBX2+6pwia-pf%gD zKxl6c;6OcZ=PS4YmdIleKf=U=v(JFNi%^OrTXybee=1p0e<<_e-VKR9 z_!+LwYhw5q>yR2}XCk#@1a}(TzgXko7+!M1OEY;u35DJP;$<9nVPR3e(uq1Rqu< zHK+(dg`VZgAp<8L*9FrynzYt5!pcyg;rG{4qa#iVnyZhHu=CS6DzUg%fjdExY%QLd zUxc3F98O-iW(Q|kaZKgU$lIQhan&`8f0le>j8M0)=x!pjf$}l)T;W5nRqg3fW-QAQ z4D1}CuRmEoRe^mNMjvn##@t!1AQdKO5?3WhL~QrSeO)p3lODic>@O($Og-?&eV!Na zUPlF&V%f6_dPdC;p6)*h(}Mkmo6evTPi4twJ>LeTl5wCY@`VI-iBks8NEA`Ve!S(k zfbn2m6^B2{W~_35l<9rhZ%poJ8LXUr+es=W_C;jDSe2AdSJ;}IUASrW#n2&%Y-L?W zMhr=Ik#&r|wm9UaRe1YWh<$bN5gnUikGHTE+NXjOcZafL;+4AIPSHH=?iF0T=gkW_ zzTo{kgcAnZBp(C&082t1Dc3IV#}-Bi0ThE z;|GqmmuANEt(!dTZkhcwv`Zj5n=hiRg5(CC<$@POC3-E8Bx$Y&tA)u!7tBY1yLV=& z&{m7Pw+Jb8Z%A64wkDTUoB7R3|o={32n zP*HsP*eY4zN|anx1h(GaR?I=#kZPp#1I>ulwF{ZI`=H|WYZm7C zS)u4c8v4_+vV7~c#MV040T2!6>C7xrJY>9ksWo%m4D#6EVh3;6buD047LWcsSo2 zN)u#9WKB$Vu4i}4Qx_N3r#C<*BR@DMsI-6n)p&O*mF7v@Ki}WMY(CD2Ns*aGmP^k0 z*ZSd;O%@ZI7t!2&g6h^if-t>m0X9e^tNCu7Hw&X=z-3vT&Tl6;5PIm~_be4g%AKUq zl&-hyN&ZP^-fCQTp2-+BsC3Wgdl*P|nK&|Qb9&PVWK^IlmCZwD)md$wHVBmm)W>H`0)90*oNQ#4~Heae59!$Z-Mxv>fF47 zTi(_^vx5{R=ONfMDTZxK<_@6`j+J~`&8+0~bTN%SETNW|eE64v3eIHt(VWuZ!uq+-6ZPYPu9}Y%wXUz)cs@U!BIgL~aN_0 = \left< \frac{1}{1 + \exp\left[\left(U_0 - U_1 + \Delta_0^1A \right) /kT \right]} \right>_1 \] + +\end{document} diff --git a/doc/Eqs/compute_fep_fdti.jpg b/doc/Eqs/compute_fep_fdti.jpg new file mode 100644 index 0000000000000000000000000000000000000000..ae8de241cc132dfbe0d932baf99a9e066ab178e1 GIT binary patch literal 15544 zcmeIYcU)6Vw=cd!=tZh@3{nIQ5PCqGbV5LS3m}HjLI|M*2oOOL=|xaMK}AJH1Vp;h zJ2pg60YSQ`C}^UBkrIBJ=lPxYeeXHv-h1x(+&}M-+4(YiX7*ZZX02Ik?d(qO&I1Cr zRwyd~0)YTF;2*HN$m@wRH}`XNcCbR(S%NnJfY-(jA5LNs003e*Im+4EOxDv2Bg^p; zU;(%Qc0dCFu(;?5dlxHL04yj=bJ=LH(;oh3*%$}FnE>Fms*R(p>_6N8OGpqG5k&?7 zh$GlrDAO`H=eh_EG#sq>GY6s%9SbSg{h~I!%AuNW72QdT0BE&#!Gyt&j?zNKxaUmd9 z2QhDytFt+X4FQ0YH~3$$|G!{zAO)lo0L)1d@lp8T5VEW??y#(ezP_HUO<-JDAepS{ zh{X}GQ30~%Bw_?MJRSi4=6P=vAhai2Sy0Hj8v44rs+ww``2SJ>wgXQ*7oln zKb`(sGl=Mmf42Q|>_6K`w*WwI9hA-af42Ew0f3fs03bf~&o+e{0KlIL0L>%+!jI_Q zehDFyBaR{vadB~K_&}W6o|`whgRn7SWZ6BT;z(hn zm?+uk2rMp8R`uU+;{W!*e91crdu!;Q@Fuo)j*N5C5O7 z@PBjIztFG;|K8Ui5WdX>MEukMfe{e^y7mHK73Kk;KG(rJkbkV39hW<>r+FT*Pk--w z5QF#sy8aIrmVEGEmS}vi>|V3Ev#TsFCMtFhgF3NyVFS1Uen13}01g21fHI&8XaY#U z05}F%0=9qy;0kyFCjcA}0uX^HAP%4cXMi*y8#oVK0!n}~;5JYRJOJu}7N8yI0S1BR zz$@S_Fb&KD%fMHF25bOZpdsUc@Iizj5)c?f5dw#3Li8ZU5KD+1#2MlRISC1dghOH= zRLEIKHlz?z0=WsPgw#PELwX=jA)}CYkOjyJPH1{ws7 zf+j(;pheJI&*7>YQyTriersrO=8VqEn&UK+RWO| z`kHltmBz|s<71O%gR>oFL$P_X1+&GmrLh&U-DPWH8(@3Ow#>G{&dx5%uEdUHw_*2U z4`oke&tbpDUd!IiKFYqtzRtnHA;AIXFye6Fz;ci|(m1YgRC9E3jBzY;FgSTQVVs(r zR-72laLyFYBF_7qot$HwpE$R;1h^Erj&eD01#rc4<#XNUYULW?TISl~7UWjqHsW^W z4&^?>eVO|K_W<{M?w>q7JaRnxJWf1#p3^*+c^>jS;aTAM!z;vlgx8$chc|{dkGF!i zoA({>Pd+}rLwv{hFnnabJibc4KE7E##y;VFYWq<80`?{EE8W+;Z*1Q;elC7RepCJv z{0aO;{0;mg{Hp?70*3_51+W510;K|v1ttX61%(AQ1RVs4f;ocs1)mCj7UB>(BxETR zAe1UpF4QNqBn%an7d98h37-|dEj%E+EW$3LB!UtN70DK<5qT*>+b^_Vd%ydB%Kp;* z9sB1+p`wRGQKDg@`J(lrI#Ie@`i1nm%mEo| znFyIHGJP_u2Sg7XI}m!{;(^WsD==Z0F$@p82SfA0&TKzE_^608_A6pej@;Oeu0H>M4dO7Ap=Z{ywC1 z$m3A@p_W6RmBf`$N(o9;O7E5VlueW)m2WA(Im~`o?=a!;wZpHDupH4j5^|*U$OxPT zt_#P*ufa!E*i`gY!c}gmOsMjznySXCR;eziiK^MDrKq*2eM2Z9Fo*)g5Q3?$qaLPy zTYXwXNW)emMWa>YhvpGYoMx%!8!bL9E3IU$M_P1kxOSlSb?r$VVI6y&be&$E9bKeu zlyLgnP&FVJ+&B1asAL#u zc-wHvNX`grbkk_wSl0NY@eSj7lY=H$lUpW>$K;O%9J_n$lj&j8P}6GDZ)WOdQD#kM zzs--DpEB>ZfLd5vWLdnl6tZ-)EU}!mlCui7ssTjRciXVpplu3lCQvdc9I6sU zvqjpTvh7FnqFvA>=ta9Dc2Rb%_AK_c_808mA6Gmce!Rs2a6ma+aF}saa*T9rb7FUL zbSicF=&a#PbslmNcJXt$@3P@)=9=$1?WXJ&Hgcp!lTe*-V@<@%JaFG zq!-@n5rzZfj=76j_qO!DM*ZoocSN&-?b6hd*YrwI9ivcTvMuCNapMs2n3WGie8wFnoUI{S?DGFJ|o8wFH z^iZ47ve4fI2SNp5H_RifmdHswNqihG6ix{5CmkSBNTU((h_s0L$fJ>$B56_RsJqdS zXy52ZWD(GrdJ&@>b1r5f);P8_mJ#P3*FX`Zgi~I`ABoS5|CC^ra3_&95trCYJxD!6 zT{vZW>Shuo$v>$#Sw1;6dHJ;U>3e6m&k)WGr>LhCru;hVake#8CiQgc(mCsMRcZUu zqS7YP4bsapSTpb$FEh0=uVgZ_0LF4$jaz9@S!>*B9VewUsWX&03ha~H=H&tJB?{OF3pmGf7&OF~NC zmYS8;UX{L@dG+_TfNNvdk6nLICR3JOws`}8WAdi;&E{K&ZWWcYm&cZWyzPE_=#Ji< z%Da+xv+wRygjdYpbH3MKiL9)=FMU71ilr*1YNgtz`c;iZ&7%jZ4{p|q)@DBh9>zTU zQg^a$ydGWO+o0F*pi!~$YLjqNRx_kIzM0k%(lY(S_A+sD1F2CYqPYHbzm2ir?K z_IKoWa(AY7?sg?~t#?Osul5A@EcN>JPWO5Cz3F%Ae>s32crs`;*f(T4)b+&ZN&C~I zPai+id)D$?_j&URofl2RI>Svbbze4*AV(g((tp)DYB<_CW-`|E+T!)#8`PWUZ;!tn z9d{d_obZ{LpA4A%{4VSreJXZpYx?wiw)a^x0y9Ok(zCbb4$sxj>&|y9SS-9)bXlBU z!YzIM5dC3$IrSso$D&WLPnDlFKew+~t-Si;{bl)U#MiCWv^BxCtKXErHGV(#{RPdF zwoH$r@BYa7De<%7m-esTb;tGD4dTYu?<|G{=KSP@yo1eDgwmG&h?;PG~Wulqy zcZs{Zy9?|mEh+dQ0I;_Qj)2|(C%_J22cRH=fRO|M5&Hiz=vhD{L0{o-AHy9Y^$&ak zqWsVP>G;2#iakFBob#^&#xH;QC4Yaj7N!9lpwrO?wqCsf`RD96SpID!r11vy-!P!F zH;1WoK6HjLS2(= z>tv~ocOkf9Vzg2IUaq#ta7*qed;KW5j$MM5r?pl@sE0?SmPUjP#o8QAK%qzh{$asR zBwI^MG|4GAR0AJ`BkDMLQYaw~s4#6?CnqPgEw{dxzPXdFmaDD@7D2>lVZuESL_!2M z#=+IeDbPGP*v%t?6d0}P0FMlbpm=H!aS@s%4OBSN6CbEa(h0ZbCIln=v0?t9k#PY? z>qrMptUHPrH(9>uDeBYDozUx6ug0c@oG3Ttp1F zt_2}fC)6=MCQ4U70jY(EL)%!y!);LUo>4e63_Q|HF94%sA8d_w4bdVdsFR~Sw8%CX zbsJ4rBoPy$70r#Zh_#O)2Rmy-J2*s>b&;L{8a9C>q-K0{po6`hv!!j6r8Sv^(}>1n zHN%i$cz3kDu7{_;eJonj1#K6G=C;&95^b%#wCtm>nBy8K*9amKi^D||9c+W#T-@Tx zc4+$uS4)CAMi+x}L=gf=#As^|oK{FE+B)pGv%4#I5ZOZqiE(s{33fC?xwzrX-K`?A zdIUXNH*Gx|R9KuA4j*T#8Hd2C>ubk`;fQ!Q9SSPS)FaH&F+LJaA#s}#)ZMHw8sRQ6 zHqK7gVPxkxxCh44EgTyd=^5tla$Eyzi}%8iBRy<_Y&|XQ;9x9)z~Ta&oDspA9(rT~ zH`Wu5w}=iwTaX>1!C8nd;hvTe9u{`d(V9`wF?Ix;HWBY0tr2D6h_-j9*kT<6G#t!` z+OhFY4)KJ@NE~;JhF)NRgBCiRY#Is2#&{6I;zO{APA9JCIASzy zJdWF$Mfyjn>jebqn8(_CY2h%KD15ZFR#?2gy+)j40=KzsU{ny!O5aXT(+!lgj;;$% zgY1T~CI?63EbQU#cItZJj%ZD!wPm=wu1zpL#zHGLl;9j{or#XrI^%=35{-tIUu(%vp6ECLm;;Ti8>ZRf13W$PXs zhek(nQ=CZpkpvyI9o{q6(o9F)R5J)=9)^n|Ygu{V^*uGw(P8>Fmf^P807qh!x=k25 zDgx$tk< zdRgK1f+G?Fy)-mT$+$RdBw5ej5seM;PvEwRG}8+S)AHBTh3n#6Q6A>%LBs@YePjrl zXqsTA9~|yZjv++rxS2&*MLOWny0KU*WSm#DU92lkE6~eBom)T1RyPED+}1JFGBDnW ztfA+neO$xYHO4C}LMzHF%)!+?TH8J%CY)%Az{KjgXat8_gjz))Y;X=vE@+II8+W9m zwneZDh7|0EB$>JD*~ht>Zy;lbj6zCkCRLZ>cM)pBn!M|h!w`!(%Qo%1Qiu& z9TjP>rS3{5S?X(;+2~q3s(Wgw+XRu!5MEA!+@t`66A~WmsBecuc||yS+1X)H{vK!> zxSgZ6i%ncK0#7sxK|5PVx`#y){38jTF+^<*bG_p(=)f>Hk1!lJF#_dg9)ODs0e5?X zbAooLdZ>e=Ce|M8XT%NcP6Oru3k0(FVF5p2fwDpO3Og$+l#PQO42ZypiG!1ei-VJ! zlbxN5kBgg!hnJU^gNtt;AMZX8^6X8rHx~NWST-I`c1|$H`9CbX-GCq`paW@yLgWAz zK?qb3vfB^9z|)Bh3{b(cchu|^2n&>z4WtO91MJWw0Fn=dvVg?0v4RmZ

-xU=?H& zI;dgFF6@Nmkc$-2JX3I!Q{JquXTS3(O+m{)Dus(%R7_k#Qt^E2+In(z0M~!leDrhe#()U>Vi?jb4V=4bF&i=vJKlz#hc%h(UA_x@(On{y3TUpA$ ztx8XVXu`GS)uY6>9WSP+y|Z8RmiLXC7bya?IziBS33()R{Smh#`VeW|;v zsjPPw$bv~4n$x~7%=Png5|RvQSBbi{3tL9c5=}Bjg5$_|S-$ooD22$nLBUCRY{q`2 zH9z{7i4DxoWn($2?S$&^a_wm<@*d^P+Syb>ZT&P#{Txa*JX+jz#C`wI+HGO^4cI7E zb&G?lOBZb;B$iV{=;?j2**^3)5#3CsrZTUB_3U}IpuA&VI#TZ{Tnhqnj^z?2kLkEk);V z7n;jlJty%1ih5_VwljaxY^X0;$_AUk$qtFPg7QaViY@(J$UyJ+rylUoY`%)?{bF*hmUuTRjK zHQFa&O=I7w2)@pO$lLe3Rj;`lY2ssS4ra0EE?edNDHemWs5LOTgXyJxb26Pu$nIK+ zkTQYw@99&CF>_TB@r6Tg|5&Pz9Zl7qZooV-AO7}{WcIGgOg;qKy=V zPW0^pjd3a4=q>$8s&D;74Us7mYAlsMF#6RaYy9ERosNgCVw%-AF^U2(^)%q#%VTnN zhF)7(iuFSN>M(&$SRxxM(U7U(s`KrSnUkYxNi(riK#!{7zBtel8+# zMNP(k?r@&ckMbh>g3gx}OEx2YRr!Jx?w848gXE8I$X|Ws7H7&Z2mG#x#EuQC#C~}G zBQ;*ph8d&yHmdJK7elsUa4l{ze_Ob$@466U0(a^z^%z4bK9V-lzach0D6tm&I`+<^ z^Wi5~$2C1|#^9O_2Ip-)wv8|pmJ4Vjs|kj1yiWgSaNl=HN?T8fNg3kuD}0GxrVgA( zTr<93w|ShF^RxNj(;NJ*J0&J~2cD#HKQ0w2j#jitoAg1e-kG_y(|`#*sUQhs?*Uaje3hW9St*PRag$j3X^+I=O=3s>ZOSw?#ig5>}-)-g#2`jyGvd zp5Xhjs84ESkW_sv4+NYtepTq;SN|FK%a-ri^DJd(U)TH%zXR>KEuEy1vjcw6Uo%k8 z@wAq^c&EwG&e$0<^z@_EwHoY?jCZO7%fr`Nu6_#OiTGLn;@}U(PfYft@e>F-e|C~~ z$N{~v#xe~sx#bfImh zfvL4^vU4>#*eH6Df6cr?_s)D5n|)yQEZb2#o<2-Q zF;i%`IsT&4BU5SY$cwGg zlEKHjKuRse>J1dpTQ-%>(Yh@{hbP0;;Fou@cL9RmJL`@0o$7Yn{cR3fUP_rX6)J6C zGe_uTXAaWs@7v@Onay8VTMr6aAV!`jSm^D809$H%M`=N6I9i$;^GA%y?Ym{>rMe5G zF}d#4<{{RMWs%pG+G@ENI4Ao4@v{pBALHxn*{|?U=nhx53*lc4H>sy>hTImK0*)E& z0vjckQ?eSZNgl6U;T3StHJTb6xy1W`mB*f_49yFR4HPvaqp(o`7JhMH2 zoYV)Ks_27>F(oJ!gPrVWPju0W(-5`Q3vbrQ??}lD2fYtwm*%R?PNE{?L8ViD9pL?` zaOMSE#euh;Nn!TSNrCE(0S$K-Xp??YfuqIez9sFO-L`+Nt-eX!H2RoD_wk#Z4jLo7 zHx(U>=lWrLR!VIQ$`1Wi+ilE4>slS9A+2b?)A@?i+ok4ZxcQ9VRg?vGmSTee3r)0q zM8Sag^ER?G>PrX<;xr7lEwSZ7m40O`%N*&Ht)n}f-F6^u)M&Xh;Ff)4{c|`^N+PYT zbC)7yWF*AdojC}8*XC#z-=|s<}f&i3Ei~t`cFDkoS#h zIE3^y8SaNqWM8qr-A}9C-p{eYq`l1C(xh6`*2+?o^zEzg#p+X1*`#xwa$CHG=J$H5 zXAnxDKAuEt`jKhWAwUnQp9GuT$lEFOm{J!ex$7wH>$sKavJ-XVj z2XjfgZ@4?5BO{hezYRzU+c9bYy2`ZC2G^e;Z5BHu%N1x|! zRj%%zxMZl^dTGqg(fib$G0xfG!I^$JS(Q((0MshHyKCWdCv<2#qpR`sF3>8m#Lskl z#W5z5GacnQ?;%gaEgiT;I>R|9ABeYHUP}8U=mMT_9b|SdDQ(^tPeS-4V{Wq#D(2#xFu#ME{pr$|*R%c@NwQ>>ce zzcBj=nnwo`7{Zc&$X9#f%&`>%5U1OcLCP-j9}toX<3Ue!M~^LlWor0;l^5>)lxmAE6_->%nz&)Nlc>KaX^w>I=>`~xHD zRWcnFIgR~~9yhuNGheow`L{JGUPAvt3J!~I0}If7;vNGqZjjc>;$*($ko@df9mcgS z73S2@T_A(%R-G$_ZXIO`&OQ$$EDY=1&9+aGP^4VxuXjkkR~J(7b{&~o>?x1y0SVRU zBG{X65Ox}N0sP|!#+*r`Fy7>#?~<5Vs#jwxedM%SqbC(v-4~`XE-O@~i8!<(r!^Q* zqL4G4;cRkQ3pj-WiN8$G@AYJ=FyCC4*tyi?myRy)p6%R$#L-653%xUH z){c)#`QCZfc>3gv`joh|S}*V{O=rHA{JlE2WpV=1U233;Tdc?$TSC)oIjQGhAd^ zD!Nr}UbyKct+y36702XSfeo4DC4A31#8BFjqqJ?g_T+jGUgu`Mnh5WYrCTyDL@vX$ zNJUQii`qG{H~1eS`7!XNUEp0llj~y{H0fxF@!|COiq*^o*lL4u42g{a-!k!S67qg7 zwy8RF(XeASXz0`BDbv}`?i>6gy8uI9%8CN&7T)2JBmVV;ng)L^8xg*@C3>#O+SC-_@^rYf$|1)-!+(NNPb3jGG{;csT1C+A zS{Ht|rG2|oOSPX+xh1g$U)i`%u6k@FwuaX}x!IAF;|Q@7`KxmD?*cT_6>=>sY0y}S zQMtf)uu!~|4z`L@X6fN-k{;Hl!au$g`Sgvo`C+qtdH#jD{l5@vCR>Qfq}NA1(s(!b zbV6|v2K`#V$nPs*X1qGpVB6uT)Ep%Een3U&cF{zfdb@M~eD&=dJ$JvWCiCxuIGCKD zXm{L&p_Zo>ZDzIJ9A)IY@H*U75YA8799k^y^YvbYO*)+0PF(!XDrKTI%)m1^ zZ+LU_X3V1|QQcSG?e%u&cditnd_P=0{sQH2+OIB=`Lc_x-FLx+o9e-B0_4X&L07iXNI3d#%)(H3+Y9+eY9;T7;S>Z&+Qhfh@-^I0jy(L2mF1lrp*0 zc7b}6ZQ&s_BYNuqVOE{KQ9(=Yk2N-CB;KLi|LKtD`MsKyyFC@=Q8Yf@iJ8kptVw#O zowq`i7D%qvQaX078N#;www)Os^ok*8%Ho%~o^ifP2BBB-y^_Q0#%sr8hBmIvUQs!W z+_);JeO_rwqG;~L#oPG9n(iiPs@ijs+Xu=PmCkmBeisW(f;2Wi?kMXonn)5Uwn^b3 zE-reh4PIK7GxNWwufife9ji{bNh|KD@mu6S_iHV>yR6Z#zlLD(cCEbq;TsjPKBR8T zLz|n0oHM<}9YH0wGZN0F0wuXG?6`f-yq>*`sT0OlR++%e}Vs_2?}zlQA>G zIW^|5>e>f~$*Z#U_j*$lEFgl zDWFRPq5V0A4?SO&yM1_R_;3L1OK`)4%G>u*`dfw*@F4|#Xw9h>Kc3{CXR7dHwii3{uB>WE93F{N$U*?fTrA~x}uki^>dKvBST;Q*Xq z@eff){+6!!@+5gi%>rrCy1!FzC%^sJrb$1H1^;~UD*-t+|AuI2zyEenV(yWT9JzNi z-diXfBVL#2?{xAy_P+LO7mKlG$Xugej|0c{F-D|H10{KIQ|Efy-S*6Sb5b<7{eg9+ z=(Ow;!?Oi`hEz{R4P9yDdTEazc%TOEz=x9g$tL?L2{MF%IYAvGmQSe1v~QPRzPe^$ zpR%DCI3A>7)74?;)o-!vTOvXQZKM3BKAFS~7n%cTlHP3%l&EzC?j;9LXtrf{PhFeI z{WQ7m!23mM%c=+aM#)s>!}wZcG(kPH^qIO`v*u%9-DJvy$*oU|+pwpXem0Szx+GSF z#%@Lt#8z-OLNV1C)$AuYbcdBU9FKc==9&VFcTpyP@j(vG{sh)8*tQ@nm8!KUMcV(l zxCEB_phl(L=$_ZiowvSNQSDS%>pgAI75+s?aL5n{JPa+tU_$vfaKH=Th%nW?5GQ3SR7`;eCAgtmQ5Aj z@?*sHgNJQBvgdnhr~2z~%%}c2;dcF6(^EHQ52h%BA#!S>^+~1r$DR6VUWzHAS^P+? z_Zq(Qu$xR}+FPRH?p^(<3hWLfgpI$dk-Yr3gtovG_a#G}O`N_Xn!ur8?(zhk< zZ4+pBT2h$@sVaYlYI;1`nS0s&o@t{KHMq%vanQ7+qsuD zhSz|!DW+d^J)KnIkW2xHOrdvN`k$9K4WFIveKoM* zP={~+Dvk9Kgu;8PCB}8|L7HPbS;qQbk{dfO(M>QD+9QG#e}ajaPlyx77u1{_-9u9^ z#}B)|v{?{L%UW6!@UbpUMSmqc8N=VQz`fc9{=N163>``m0*$I{yAG{*-fw6GFr{lP zCTIR~m^xw~y4C-+HaWngxbn*@(6!_t)vauN)b}Lrj8iZD7@U0b;TnvWDpAVhhHWV` zJV2MaMYSxmu_ms&b-Ae}zfp?vp<%QgcW=@HS>9L&TjLX5`H-@qA%z{fB+_pf-Q8Kf z3-C@Xj%*@KL_t4CxUX!xqMRvFJ5cuPL=u<=npa9U`Qva*VouV;AAFGS&W&vYy0JHy z;|iITe`TmzP0?Lc60%AsDNlkDW_cUl z%8z~+FJcqR4-aQG_Mty#R%?DTK5;a!>GP!z$+Y1l@C>{4lTO+NAcp$8z_SFC|KPFw zf~0SmCH0gbhQ1#lw9@Fs`Gzt|Iqe1ql#~*JbUg@ zvVQiK_*Vbst^Uf5ioA2A@tl0Y2K1`ckU0BkNg37UF1-|^!HVPew&zLwpbl`nI<<}#Zo)>Z`-{!DFSdRG7LQdJUn6m#wV!-+{ zaISZ48)_Fe;^@}>MhQO`i~GA^l(UO2-l*jJlq=-e#}5-J81c@h8>+f9xEy$jY#_z$ z?9ss*l|kSCghSYW_7wVDY8TB0!ADhOh|zy`3sCJCWnf6Xk#zynNk95^?j8T~mxRVc zQZr`Ls|lwb=ebKI$CN2j>zZ}+m8|<<>|neP#(2++_tTQso(C@y;l4Dr$3)`N8vCri z$}f`m7hOTV&uc2yTjrLn@va5c`4>QL)#Ta*Wl7$)3{Y**Pc+~=zxB26=;h1Y$j)KCZXvD=}Ke-UxqcihG zqIo`7A1V^S^EzO~Sf1HmMzh;`)Rdg+;l2w9mcNOSy2jBxWk;Ja*R8mJ0u?7y*mR|k zhwrG=^gCkepjm+zrsl<6xf6Oj)BizHt^b3roL1b)Gzq$wjGKF>wD7yn0DUh;q8)at z2bY*E!oL5__t@`kZ9jg?q!H3f{2%LS96-}pnm zB)+YDgWtItk!cK!F;%FB6YZ)?iGdxXhUf|(Jmy^6$;`D+nYRk|opPE?(rL2kxT;=ye(K@NcaV=dd!dyz{LpDR)Qq2kq z$PtSH-pMzWZ=L4;tJX^HG$iBsMUtL(^3qx|jAgdf=}H4UJm2?w;t$BDn+gplFU%a8 zZyl+!4kod_p5qj^EDdo<3Sx1aH62`BRgMKfQ>Pw$i(JR$#K zX1H=#tx3N8m#R=aXXF#1pKm;-nCy&mH>ggp*lTGcKBL=~ceHK!t(jpPJ7?c~bIqwfJ2q}4O!r@PWV(O{`2_zvT*LtXo1 z-`2E0Ux~S<`)qc?35oF(K=V#CKgHg&toT!-pEvabmD@h7A^@CP^K5O&|E0>&zZsPN z;A?_?QA-UM_+DfrUOLW$>G_^%XW81 z@NZ4$nh9A$YA(mtHdKAcpAPQnJh)Q=W`2^nn6Jw?8@Gmo(WAf8X!!%G`^F41zcumm zUCHg2ymVXev5?P7F~4D_XXb~Z*>7ti-vrOD^Pk=Jy+bvpT`#U>h&ewTC)-Dj$(SF1 zqY~`3Mp|1wMzUbg%}t#)%zRcFZ;|~`_PjdV zXtyDW$=N_h4kk;P5Ma}U{v_n+udaQRSpLlBSxI}O-D9nHoo#nkMkhmm*O4q`ef~&N z+jHhmzY7dbgwf1KvO9%GoA~qRAjbQ?vJi@Y;+nLJM0sELk@mKH4( z&MqL_v#y%betPlH{vP@LtCC&Y!Z3%|pvgHUJYUtK6H&maF9yV8a`F!caS+aC0ez#F)H=9CrXz4U1UawE75FqnRb!&Uel(J!b>duY{8=<_?E-Zz-c^OFa2JPziGW?ftkb4i5fz+uk+B?Fa5L#pC7Mg8B!VhW74_{*k(-6R%SE? z89aHWRmq!__m3a5@SE&ZFp-m{N+syDFgkgW36YT3qwxQcy3QzCU^|mEnvk}|TMgodd`~AVP z!1TKwq2fY(K$4)KxrV|#U?0zM)`aAjewcQvZ(tXY0AIv&^dY)6i)EgRhGWviJ8soU$NUsW%u~UDa*#m3# zSc8HL$nLa!TTjl0v3DvafoUgWk(GL%l}%D+^>^}&!{BDeTq%jS*f>nXTBlmHD-;)+ zW|AtY70$cEHZfU*FS`8$~bNG=IRz@A0Eu#kXKMrX&YvC; zCyzJFg&T|CP!*3JKWZz$5i+IwIHpJlC2vZzS)uRo&sl-zTW&g80wVuX_y4H{$Lo^(>*^mqs&9OY zYd0n0<4AYj4IL@P2Xg;5({~(}I1OFN=fq>e&ny@n8R{w0Ejf`NOb`(jjeV#hfbqT$ zk#-t9trB`)gbfPta*yA=&*mrsa2z}Q1^}h;zpbu8BKWhKDNnE6&a+AwwFFRmSyp?S zURlA@_rV{lp8==%@^9yUKtc7B=d!#NDV$H_vXmj~*$)`}=5%DnFME#xNwo`=p|g_L zy=&w)K91>!YgYzl&KIKb;-crSO9W(I;Z(_cMo|DotCl&h%HL-!H@;5d4VgM#T16?M zd}~VlO0Zdc^foX{Aw^#;z)>>D#y?LnSmD0hy?KbYw$m{-k-w|JiRscRFFC8pK(m|8 zY10K09A_C5BPR7NtH_$9k*@lYRO17b?8S;q9jOtXLAeWVuU1cv7VTuo85Wv>srlGK zyeRtdog#cd;m0o@?Vn3o^MX5OjPZLz>mj3@);D;9hf%OpmXYxB%+kod&;ychh~Juc zqMK)bu(w=Vnhw`cMoAH*PbW$aGWKsNf89i^@e}CCrP`dv@1m6QJ|<^+cS-WbiPTM< t>d2=4IOK0wi_Y0vH<1(V%>fB{{jEgEII%H literal 0 HcmV?d00001 diff --git a/doc/Eqs/compute_fep_fdti.tex b/doc/Eqs/compute_fep_fdti.tex new file mode 100644 index 0000000000..fdea6faa3d --- /dev/null +++ b/doc/Eqs/compute_fep_fdti.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left( \frac{\partial + A(\lambda)}{\partial\lambda} \right)_\lambda \mathrm{d}\lambda +\approx \sum_{i=0}^{n-1} w_i \frac{A(\lambda_{i} + \delta) - + A(\lambda_i)}{\delta} \] + +\end{document} diff --git a/doc/Eqs/compute_fep_fep.jpg b/doc/Eqs/compute_fep_fep.jpg new file mode 100644 index 0000000000000000000000000000000000000000..d84a76b0ddfcca48421c272f9f7fe64a6ece5cd6 GIT binary patch literal 18055 zcmbTc2V7Ilwl}=#U8E}rL6IUY^rA?lmjIzxA<_vUgr0yQu_8r8Q9<$1sEDYjC@l&| zq^pQX7myYd6p1935J?E%<~jGCbH4lD`+o2D4!^zmXZFnAGi%nY`L8vz`C)So*zWG^ z<_z%h@d2*jAFxT240dyHKzjQkoZUQ}zy|;z>FR+>#`13m08Da5ny-t!dT>any2v|# z9}okC0b>A&j80GS^mFzHz~tuSpq>sE+QR=ztT6z5695bwxO%Ir|11Ch2+2gJq-6jA zpEp?AG$uAZ8pNkSoP^6r*~({tSUw89h4}@ya2nV^5bxN+@&Ca3f0y|OKD32nFv&4s znXNXb#9(5!a2JU4vod2rEZ_m+yew2K4#XoM-kX$(L4lYJVtGt#WI6x{N^a$6#6~B8 z*a*auY5u+rAhrPjQOWp!!%_c+Gh*>zI|0A}o06S|iciQ;*NNVzZftFBrS2MwON!0N zFz}9yMn|T_s5@XWDUr$90Pv4KZ`A^1w`8jh3faQg+QP!X#1It!KhyvA;Xh0L@4?pC z{-eZCpTEb9Px0-)^8Qu#UwPQu0ATeSl+F2n8E_G!6V) ze-yX$B_SgtWj_>(!{H23vC)QG0{v(D|19v&lK(UKx9=Hleea*LQ+JGwi_A>QP~Q@2 zG&TvFnWmne5*ZzbN!r+|Px(NZ|fHWWv>;%*R4L}Dl z089W&-~ez4a01)`1mF*Z01-emkN{wSGyn$>fa5?OPz0O@E&~++8Mp)72Oa};00n3T z+JPRR4|orZ0#m>o@EQ09FaQ?70S%c5pA?@Q-%dUVpC+Fkp9!B8pDmvgp9h~WUkKk3 zzIeW5zDzy>-$}kAzEZvlzFU0v`JVDU=WFMC%{Rz5!8gzMmG1}NI==wFB)>erD!&## zl;4WqjvvnN&mYbo&!5Vl!+(nZ9RC&m+x!ptoA}%L`}jxs=lH+z{}uoQBm@)%b_*B? zSP3`?AOu1M;snwJhysNIWdgSa9t$)J^a>0M%n7Ur{1FruloM1JG!Q%>=qeZ>7%iA8 zNEAFPSRr^%ut~5>a9D6&kRiwuk`me_q$jjr$W16%C|(FBlqXasbXTZRs9R`M=(7+@ zSXfw5SXkQ*6H&LM%osTdYLvj##tU zfY@g-j<}4tw)jDDfAK`|?zqw*-qI7IRQBhIS09Dxs!5t@wHQwUVRD_m1}p)jW?ps1zjrkJEyqFARmrns)8s${1Wt5l%$SZPRUZHLN^ zLpx%36z-_qF}h=Yr}|E(o#>qxc2aguD+?;?D*Gtoly4|^E3c@?s~k{?Rw-1eQ<>bw zze{(Q@2;b}DtEoz^;=a<)kQT$^{Q&8>WZ48+99<>wM%MkYF{C85L*ZeatT6(EUPQ1 z+o>n1Us3N;XYAg!+jV#5?pwRx?dI&!-V?Cr#Gcwc(;DI$RvK{{moz#w7<(amJ@*p! z*6f|s6w|cQOwcUX?A2V;($)&nI-^C=`l7u<+f6%1yGHw?j+72eCspUR&d5IDeOCL> z`>yYMugkA%uA88HO?N<#U(Z4hrFUI#P+v&jT0dF;w*I(*q=B75mO+idyrH6@hv5lB zis5(YUT7%v0<;&(Gcq?yGP+|lWh`s#ZhXSH+4zTvu1U1XHIorjDN|=tlIb&3rkS2u ztl15-59V^_p5|xFJIpsMEG^P39$S31+-rHn@-NGAD|st#tFu6E3eXA24Cn}y z4m=!qKX5I`F{m_XE*Kh|8{8M79D)jY7Ag`N7x87c!88gMk4Ev2ptJJ^56(J5)pYj@^_S5)L&7IXou+X=x;HHVlKsejXfA!8oLyC zFs?N2OZ>t3i}7C*Ufm)9^;Y$d8#EjKYLsg%Y~pLmZemap zD09z3o((>Cf8No2pt-Tdu%)_nck8tm3NK39#M@4_ZBlcnzh9=jTxpMQU+6$~Omzl# zj&%8Sz3YZ|zv^-B>Fl-ZrM^1&s`d5$*U#Try`l73^fkRTf7{q^-rxAn;$72#<-oJ| z*6*7KZ3f$hU_A18ZX9Uz!Gq-2=&DPFY%)OX*oPSI6qfISDFMRuy{)zkf)S}d4*%D;w{uh%ktzVtLzF!Vo z{`@WF8)qetE<^w8yUzE9)kCXq8NrOt%rxfakF!5_{;d9G_N(K!_wN}NhQ(PcWbb6( z`(yQ|cRgr*iG$;caIb9a+i2#&c^@}1o12^S!X8d|R2%?!dIGv28xRGA`Gf%h5b=SY z1i&Zz9~fj7e99nK_y@-bDmdN_%vdBr5g>UmjX zyo~XwQO?mhk(l6MREk}^y}d(Pth1emnVpYMLV!bpy(20))i2lq ziuV&Y!^Nbcvfx?1S>E1I^VCpF^9(4~B*`lyBsnK&Nj78MkLj`c}(@^^$=Muw*Q`b6X0W8B2? zUI9Kyp@9LoM7JDYOpc$i6D}>uBNCV96m9J4><7;_viEdPM8#uroT5?bSQFzUAICJk zq-g(p8U}|ih5tHMaVwL4#9A%Xm<>=ytg}OV1 z2AD%LymBH_t+JA{p%_G5np2>QgLkN>alD;XoIA=s(M3GT+C9nC&)WnQ>tg2amuZeg z#3uM98l#epJkzs%5UwUE-rgxb@N{%)00y1vm+YAWjg1R6LwN*vCMTHaMT=t{EF>BF zG2Yw{k*SxKlaihk>7N$qmWqitv&1DNM|oz$Q!;&=f-!-qR{l{Y;z6mFMv30;C@)KI zC%i{ON_vo!PkNAlOme7;e@sjk!Xn8jC^b4A9T^9W3(WD)G!M-3LVG9Tg3xBhMw!_d z@q{FgSh%~TudfRn?(UxD5`xY)c5w@hOhRF@LsFB|)8KHwBrlAm8yp|(8k6pklarMc z=?DrOABFJuK$(e0Mnc`ZQynsbjLf3_@jg+Bsqq#m7~>c-%UHCrX}W71G&RsI(l^uD zF%s_TWP;C0wsQ{-bns0}bFoiPcXtra@%FK_2uyPEkMfGcq^J9U*1+FR4;~rsk&&Go z7Zekmlj@zG6K@inmE`MVXJq7q$}ozLk9G;MOF-a!5}d^C+&o=8tlX0_?L30bTmsFU z11%iA^z6N2?XqGMGBbSQUE>ns;^KY0v2brQUxb-`DAXYoYUdnhmmG(4h_VuQ^nf}B zTiQ8VTcT6bQj*flVz6e8dU1*NY3Kw?l&`5P)CKF16qFd0F>sF^o3J_ed%VVB^NX7A?j1J4P7 zTN*hSMLR)Lo#8<)m_*Pv!c!7Mt=#S0QlVB3;?{vE6Fc0&gW|yE6yUHGwfc|5&(Fut zFUY@@1O)^H1ciizg|?Egu&4-lfj>mVMMTB6lCX%lgt(Z*){m{1fc5^a1y&Rj783ru z$p5d~=1V|E6fo!eBfz%@;FsYOkm1|x0wCZ@B=nEQZ7nNXiH{#_moV50aS5GC1O|a_dvr`}Tzmp5F+C$Q3y06nIeF@I z-kJP@!qSVEE|-;Gxmt0%@=n#=>U;Me)YUgMHc_5EZ|>;q>h9@%_4>`w@W|-c_=kzf zdD_CK&x=c6zAiI={QUKswZ{IlzSS>q9sN(C|3?Vmzw}E6>=(bFpn#yrR=@c8aa$di z5fs{OEG%p1BNCY^x5wnTsJ#7!TTk1?G)#RN3Q=i;;);9C<~5mHUHiLd|7RUL@qg8` ze|GF&{h9y;P8 zR8>_&LUQs1mB(-L7wX*PZ{y!+p(Y?pHi3H9RfZbkSj2WlULy^mz~*=`l5&CyYgY}X zd@6o?7Y&`6rVkcVFUL%lRT)gcOLSHDy$^FwwwWSP(Q^ZA9TECzjux*2B5ota@gRQ4 zQWAI>YFQLX8EmXUiXmz}D-(k(%Co+v-SF^YU88?)Y2vu_bq}7wt+JkoNO3H9A7*8F zyYZH+>qViA07@6MfV_>j`y<=A7s19zohvv>Q`r%(D7(C`dU>*G$|`cyAd?Qu7(X44 zk^MTaA8db+^ODq{)J@un?{i>K^I?&jKw*T!V6EyHNd~=Mdtz~TT^t4H~A)eGlv1DNgCW{`1+>T5swmaH5g0b7-M-k;4kvs9tFDpWR!{ie&b5 zsZ~+ypXl(fuB^@Hb5+65xPoO*CR8Buxo+u|vs?pqE-k)c+$Q7!+JZ&FisbE zgBDPK8YI18VWN+QAKxjRHk^o^g}z(b_SNW9<@mQuK;8#wif>{4#lRig1W>CdXX}=V zS}h+1vrqQ6K}O6;qU?&ydS2&9as#adSEW%@(jaArIXt6};qPHFKJIs4obf*-eK%oC z!Ty_zjpK<6F~2QHuZ(hRq1~|KJmvT1CCVl8U)BXf5&2T@`t31Ztb_aCyph%{j~Ndw zo-VGQRBdgEd49ASejLj}wQd4)@$^{c(JotqjRqTmg%WX;tqHTX6RFUBJ7GVzv#V)n zHM4PlVEMfWJHgPh`=8y%un)sJHKzuW&(Z5&pB|PyT1zK0$t=>wU!-{0F5-Jwqx6|; zzHI1R&2?B;b7}8<^>|f%#mu@$!wa~-OD=2N*6G#NAfs&Ctj|9v((kCCTo?hc4+1o) zb5xEe@hz-wpqrl9Nz>5msa;s*dMx)(}YM z4rT(!2hBd?lsaKlY@LliiCJ?m=Opf!!TsS$rG2{+z5Cbx= zb%IQhJ{EbJ>r;cTokwsrW-J@sd{(IAGoihB`#t*7KM6&96FzKva0nK=HOP8PC6m`! zrR;Q$I&T1}NJ1fsOu|VWQu7A8f2&*zKd4c<&Wmyk9Lvi8UZgqQ-`R9W0YN?MvU%AJrqX zy%uu5$UYtudcwEfi#97aax!~jW4OGdTgy`W>7@J8mqfa}H=h%DA+@-g8?{6gLOS~o zb73y1qZkr8Mknsya5XHN7mn*U@4^XVO%{Akh~%M$cFgFdnmFm-w}?c_ zffMi!ahPYZafKQ)o%n68>3($>Zv?iz)$T4qgYBSJwckk&UmpHEOl2PtUlpX-zSx!# zb7U~&m1u3%CJ?IA9@QqsAQy0BANP{9itl{zydR-eUNxNv_-)XS@Z|YT;Ix6-&%n`)0se2R5=lP^ zA26mdQuH_Gt%a+FDQZn``-I)7{U@mLf(8BYb z^Cc_&Rm3r}%0n(<4tpv{F>A8;3sd{_Dz%~Eis4~>-(`!k!G42Mp^R*gcH6giHY#81 zER%ggr^9B$+Oy+RE{3|_cKux3sd4g^u8R-SlK5eAZRO8RV&X}%^i-vAc>0?`>1 zv5V>bm-{LXbI&=cVo3B>UqVTe}k6oUQ)KBGJDs2z|M0z z0(tB;(8`kPYdavj2w3Kgf`>@FMrYvH`{)I`ryR`m^g| zCwwIR;B`vBrj-s4a^aOITTKS57JUy-c-^a&O`Xmg^rrxs_u194!9mc zzq1t~#4{}EI~n8-$WB`|a}HZ2;)L77y!&?%)zb=YYKn4U9yR*VX45O50y4k6+2%w* zZ32RS)nO%hy)}%wq3<-3B-fUGeSw@uRN?q92Ayl{4(wH*_l;16ncgZkx{r}pf8Xgr#G94#AEx?H zC|$RsyZ!10!`=~MWlp;=gIG%&6>Z|*sG?jb6WVoS&v2{f!jykAgLs21-Rh8;dEaz* z`Kxm}N#Um_oon?bt-|sLcg~mxXtnWe)FfB2H$YDD6f|iG#Qw30whZZ0Z6ZtghcS+*hS+U_A_Gq9cH0;(`kI$|O*hulR~oenoFu1a8$ z5=vDL=nTQ>&R@#>PrRA!Zz^6)=QS@+%1aw`xiY0E56sPP+#<7ru66r{adEagZH=1- z4S&`2WwZat_dO&saSktS@yf78t^u{c%11OFc83M4XY%`=Y7Xz^$U&Tfh94k-@(JyY}ww6w`^qecBAVfue zVInjbehalHZLPl&Et?tLO;wS#?C7rY2pOiu$w#5N<$gn%61nFhpB1G`x(PO|dA~V3 z=!r?k+ITVFoSVKuSqL`6%HSnBzkybdI<;mR=8{{D8c2(X;GOi}JalcKOO=X>B-{(0itS}pd|xz|sg_8*PJLb(3Q`z|@?w|Q0Fc{Kgpao1Y|O%8ft@7USc1 z4&+kG4X@2CUIh@oWNZYx>`ix4ksgFhOtJFWnjAFmHCc*;k{0odzDL-`+yqWt3@)AZ zM`zOtXA<5_PewdmDk2yxg$?Y~f53cG{C<2cXr%>gL_AZela5^&??IeJGTb0j#BU4a zF09hW<(yMxkoqcmciZ*Kkd}~y{jn`CI-0wsPPwJ(6RM|HfA71P@N7@3HcyPii6l5| zoX&u<_0HwPj?|VAWj2m;cUFEwHUzbYK?*j3ZP3=eWiq*cg`?G!-R?+Z(A!%uV=3LO zf8aRN@6k=iV9~I-vt(IVJVJr^j=ZB)g0r8!&|YySk6_KD_VT=n=U%w?pfONHGc)U{ z;ngOIxGAZIu{X8C3O+RP*UzmVm9X`LK+X+kIc}V5Gx*5sZ{lBNJsxS5qp9LL9!3@h zHylufc$IDf{^N!|qa$GxT~D2M;%D|jSIzox;gqm5_t*$l2a|G)x1W%(af6CNN{5Ey z>pM09Nwbn7qeO@l7xr*@6&Ih2BSojjDqfWgQcCZ~*xtAnTV#+?uItpQrS118gjRc+ zcVMH58c&@HW3kw^ObF{5+b?&4ye$zXw$irk%dAK=Z+4hqF4vEWPDnDeu_ir$r{-#| zl&@Ll9MyF+9D-PvyN8|UMX%NXcslVKOlA%L$CX@bj5_P6#5 za^C9Pi(xai!R(tt){LBuP{2;Z-LrCOEo*lQ+k%)sd16#FGkw9b3z@&l5$E;r_A0*s z^)9bv0c36(zD%j5SI1t^d(Y1#Jr_(Kn3gyMsaHAk2wzJVU`Wqv)8ULD8e-)qbD=%3 zO`YvVo7N4793HAw`dnuDIeZ6U@a?(#`f0a<3jN)-*WA9qAgvT}gu_5uzk|-xaN+FY zy_pf4xO+Hc6G$fPVW(~s(YD7-a2lWe@JrH{Up>tI5V{d|Q+h#zC$^i}ODpHfAX(p; z(%kJN)&NuAlq<-zt+dRi#*y-a%I$TMhgkCyW=qqjT%MQrs|CG!eNTT-ds2}#-OIuv z`)j#MWL6X#^v;DWN5Rz?%GQP)Hxo^UVdQEY7N(@tx~$pJ^CQ=zMl#_|9&USPMBDm> zZ`3MHK8`N*{i08){bfE^A~}P%Y$tAG6t5Qk_RQJ@+=u3d=myp1b%pGv*OsudFmvxi`s}i_3*nHxlnC4qXQq*J&3xilSHsT?_T8YRq@{))^5!?q2YCq$o^oRQBv8k8`o zpuh^Nd~@$7<}Pmr0(u8?Hz5tH`R3Goi0CggLNt`X$8;+1LY!z;VpUyguI`#9zLEUc zeKd9PPiSBXXt?ivc`b9nP_t|~tl+H$L*J5g0jaPFU^an#o;FB4o)WueDdd$2(2zdg zc+zT_ZGLK2)OLS~5^td5`t`i3`LO3hVPQ`gD%Emd*PI?V-8t}GMo~joR~PncoC#%J z9plOIMrZ5GUt*OAmc>LxF5>A(!>lxZQ7R%t4JsSlF?nn#IjOC$&W!9yp+3+1Mi)u{ z&@bV5s_O@k{)9N#3^E{k*>+6nEh+jy#snaPme23h&WaVNyFuQD&P&M<<`QsZXTz7ls15poraBJU+qY!x_$ z1znb4Q&PQq=jyW)GolpB1ACml+&*TzcjIiE#WF;Ws7GqIYlAGqRHB&ItB>)F zx^I37DR)QxnzkivODLx&61xS%N)7B+{R$$E{8-d3{**2=wTx^WrwcqH4p7C0{TWK9 zmAXi(Hl8(hbF*jE6b=0oCqK`u*5A29_!cjSI{5q3y`7I%l2)}RXS{}g-Ke}5_BE7v z>%rkWi$jx2&n_E0y7TPvWxKt5Q)>=TZ>z^ezZ4vwS38rwfSj6Lp!ATZqyw1abX5lI zB~0)U)@C2$n_bad?T5zP#5Z`2=Fv>{!%V7lM1QvVLRi)H#;U)xzVAqyN(mZ`m;h`a zfm&fi9GS7*Xdum9fz&C{^_YmRIy6kK)oK1uC39Pi=JiK4;WLvFhl4-5eGU^kZE8@@ zD11?OFRk*oQp)ez4kX*MV>pl<&k=Rt7~s#$Q@W+46KA*C#M4xc?rYQL!p2&yGasNr z^Pb;JRK|QtkC+In8h$M}bvKxY4}Yrb)TTbO32?%B?eB^2XLo#W+w+>Ui}+^7V)m|G zT;@O#c^j;WYwvNCnl-NG!24{cq69MxJq8P0lMW5##<7J!Ri15RyD_iL&vvE$ZH<+c zJwa<67S0gqs9jmzKEXXFFmX6r;xoKdcx7W~bp0|D`LcPni+W~#?SzdvGrEf?GFB^T zAYDk%R{LwR@v2*C;18#bs!__jdr`Rz*lP{?2Tu5*gSJ$C*xW;ylC25XkbRJ2lQ3I9 z(2GI7B<-@vW_ET^x7omsR^dq=W6>|do!8=Ssdgzfm5c8_{|v$i(835Yxx)TB-v?Ig(&wc6)4fip-+ z8y}|b8cpc&b&N9pWEX3U6>3-#d+%_!prXfGYNB#yc<{|8co8aD#^zF#w*Z}-4{6k# zrKi`h_2#9ya(=9*4D*@Bc-k1aLRBy1@*jZhu$#ZGH71g6Fe*!`zgvmRV3jcnUaNUi zuloAMeMQRi24D)X4Z!R}HH! zpBpW)VEuf(`wyMiofbEZO_d^H8~d}Gl+e5l*FVJ9bIh>t@?TC?j}(QG7bby8&>O7|F3 zQjYIg6`hz#Kt1{@C2z94?)lN9?rY9*<9bAlq3u9U!Dak+OjJy!^Hr_(4Ul5Sdm>pb z8y8{m)QKV_yRinp6u@vf{fKbDvas=9sb0-bam*{nO&~~I(n;3zz#TW`*3xGvn%yoQGs#$@g zj4Sg^pIo2*(_ZE0YUpSFA3p}Y*#s!ivzaPb_C5$#7Vb4{E6a5r{RP{GuZbIgG~?OmlUu?YQOI)Z+WVV8B1{l}lGU?7B&78tbdX4Wsvp5~g;%7((aOg}Ci4)CxHHqkgsSz|rsfo}tWmE;Oaitp#CWnt(=xI(%Y<4CqG>7-$a7pn$k5J&* zQCHq9-;){r*|10zX*1&rvM)3Gc;eQeP90+Q_Cgf6nZvL+Y6(x0F-<*f*e1?3E$VHW zEPi~svhQwUj%}3+p5$NdN$#%*xe0krc?N&&dZ8-F@lPddkSzpq?;@BGEDkv_%))Gx z@(kIC1?b8I$KrJjz9e+a=3s3fmR79W2d{5<&JL~UsVFO3|F~ZI|G3v^c)UVP{|zY&!y;Geg~fq5U(@QlrnDY8o| z+M|?rs7@#IO>qZR6qbmcq|8(D31BQ%Fo6Bla;2CF@0^htq$V7|>|dLYnHBz>!Bjf) z86om5|MsjCXHS17_Q=qkncP!;>V-otlo@7H?L%r*tqA)XO@u3t1-EuM32gM-YQBve zL!u`_fk8g0|CoT7uOUk>N0^Rgq!N?O2e zFYl6O>ke>b%I8MkQ?9+-pE-MusJ~o>J95Eb@$#L{>aVqsHx4$w-_qUpV?Jy<3Ypa9 zma;d2`(JWMT*YXf7zJJPH6oV|PK4D0i=4w<(!Y+Le$E(q%iRQqcicskFK#SV5y@<7 z=NeC!fh*)f@3LEb-Tg!_;?5-kThu(^D7LR$8q6>2K-``FmOHVLG3Rr=VLa3hP4uCYq;R!Ri^Nd z+0K5N%CX^wc2y;KI86N9ZWRpQkHIwf_Y22tQ`tC<0Q~khqD7D&<6bEJbPltpDz92Zlf9 zD|q^wz~CQl7${`iiA~@SxstcDmNu{fA$L=`N_gldaCIG+uO-DJKz7l%33NjzqFIB? z(cW{04V!=n3i_B0neQz$xaK}&c0KBIR&m6dTgA+Q5_(NSL|8)ia9wEjMYEJUZ{upO zP%#L$w&&eO28Sme#5};t9WsBBzEIvv5<@j-)yz#z!x813KNE8@TY@JNeL^DyPd|>L zlxiQ%u7-!zM<O~CXQ z-_L5g7zf5pU{Y41X;QEbmfGk^$N*Poh<66L`A;Vf2#}Nnf};1JDy|X(w?9 z-iy2?*OeFZba{P91|sr47zimRWZxw?Gp={jUsNAo8TJ@AFHSq!!aBNx4y&uh?)EXG zobQOe;aV!ISr)C(Y&QA}w*q0v^-$}vE6*9<=6kzUqk1-h1%=U`ss(A)>8~Lcvgq}h zTd5D1XJbA-n2inl_U+Oc{OqSYVQop{WrT>qU$BX9_Cq!SOmINzX{!Qwq|b<-%hQq8 z$opK|!AHr-(`t^Cb79w|6c%F&gG8%SMd|0HaJKqvOWG=5LTE`L7Xw;cCHCb?e8f09 zJTbHmulR0E^}7tNPwSXW+S><~YHs|;Y-ev%^@DmLLZ9-ihj|i~_sv_+M!Tr(V`Cey zWC9>T&8#K7Zxdv5x|J<1(x6hHCfXBq64iE5DeyjtZ+cjP0c@(ovDf;()o0!`o1720 zGU&b^=Qrh!A6&asmmeOoP<|8+0zS!_x~<6k*0B-YZwz%TymxFCBhUwkUeb^+;3w z1q=p5uPjtas0`2F)k3}d-?i<(n>dW6cI1a@+LoJ)Ck`}MpSIaYgUS=OF|aQa+IEsU z`k5|;`thTWDXlt3UWnD9it7@T9ULUHUMKxP=e!txQ@;;hg4w9xO3_F~u%=qN11Fh1 z@RHK3o#*H9gl)j+I2es68}MlxYUr!EHtiSq<4$L%&|(#ih4&dGd@w6IS_M`3==@^p ze>FqHjMbOWf(oU4vs|?AMmb6kLd=rj~*x0s=FmEI-g7UbhxHQ>W<7uW$sZ>q}%R3ov&qU&32Mc*zRSTP1Y9L z%Cq~rNn%*TWcNS$6_)wXl}8#2dOt#X6HW@{0iVWKt`n_51y#WHacp^`$|F8{3F~C~ zL8jIwfM_kCbZ3h(HECiOel`xL?f;Dbqa$z+{LG!HaPE%AjSA{qrLyu{LmnT#h2zq5 zVp8w^%u>5@^WAGSe`EXE{Zo!(6+JtVi-Q*hv^9R8u$GN+i%uCddUYgCw6+j7S4rAI z5Me-A@*59q_Y&L~@@j^RE}~THkjP0x%%>Yr+39784RUN{-JS!KsmG6R*1vS#1du~7 zL|B$=mj&3w8p~;;yiJhc$~-jIN}8jd$+0}$_#!eErTAm{O^;so-5}D{lQteNsc&5j z-X#cpeWP>xm^gzv={JYWqoM{TzAaR*%rB@0u6K6K*fR1e=Qf-<9+~jI1ni?bP1%u# zI|*GOmWFdd>dAts5nr7ELI@*_70VnyO-+D7cq2%aw!L3&XtO&X;guZO*@8Ee84uTm z$?>t(a2(F`p(%2v<#qbedxu@qwe}S1B^--$izn0fgJ+fgKCdJSim`+^29u{oV<+If zupMn8#Qq2)_EYB5H(z+$8Q7Bq=)G^HACYe#M^(`E7qWNPf zBk3ZaP`L8(t{Ww-(hE`!-7tn5f~^AsL&b?mwdEpONfBAT5j)XpSV=1mJ95_KCRGAm zJ*B;V@cJpc$R>(YKsa5GI=KcOF+qmAAJDsRR?FT~LSMDLtzjT&38^2plcOAY2R(dm zZF1IqLyJ*OU*edf$Rcgq2)^vk90b9DF-k4@_1ea7e&_er0JV$g2PoOsixUX`L|eyC z8)adL1ICYEhnGwI7}sDP<%y?r_Tv5Kw)|L-y9>A35Nz4Sv{@m}g#+ zPp;|)v_NP z>vH!`P}cfD!QCI0(`Mrm=Ev&_Eh&_z74yB5hVjL8SoFP{(r3BGwArHlwe+hrs4#w^ zBdCcdHq@p(u{^0(eRtv;ij+5G5VVI4u?pZ}xG_n9$U%TSNsCF#lxW4D6 zS10CJ)Gy@XynkX0KDGROG+%gB4-IX4UU&A@g>W~NY3su#9^y+aIML?rQlDz)5#^CVthnxq_N&`K=vE+wlH9;-Ue;k3I^BS3YHZQRMdu)F&+nnP; z2-^ztF0J%)?C=QtGrdF&Hb@X9{G6zak|~HM#no`GZsgbNz0U(oUo=oAv(GUdktny1 zFRI9w+EPSj<$at0g+Im|1F=mY4$0QBq!)A4W?Xa$R_u!^#6eJzr7vf^chY?OG#KC1 zt(lc@yu=@EfQZ5@MUcurX;DMI{fOs@Qz~b;1`L;%wQL>S>5QyrO!CSSjk%zjG!>G2 zdwHpSykLV&>&rk|*vffcZruLd`kH&wpWu7)eCz#A{wEeCo<%;RT#lh!5U9NM=1KA? zWy&GQK0@xs`8IjpP=q;q-@4713%E*1D?t@Jqcl zq3E@YkXiu4em%co>7@Q~}(4wnr-Z&W^`YQi@@k>Zm12`O8L-L;&QGnE* z3-01#PmzRpO2jUt1ko6O(yNI9Jx5KD-Znr}k?4aoAxKpTe&8-w9~P@LJ$sOT?s9aS z{rT#t(W;D+qqQT-O2%2%px;URO>6WsJFcD>t>z6~0+;HgBDqOdTX zz35!I(3gV-dAAN;?$hh>h1ck`*6X`1_N~Amq{tTntn(X{Ty1704OTec%+R{PIMWT2 zz_e;xoRsRBuyN5m_F_bl=AuWgLoI%I$!LCdwcv=Q#vj~DCub)QjHuS(R<6!bj}iGd zo^lNy65QTn%t%sSBh;Be9d!Gjhn~LwbzOJXy{WEoaGog$m0xA~;LL}^+x{#)+nDVA zla zBT8~g;!has^V635-;jGjMr1^al0G}jKx_iXei8>@vZRD*30hFz%~5D(KkRT5n*=+P z*;mx>%v<#y(H^;r3H`1|$xgoP-7D4BRf5ib{)Tt;A1D2`PWyqEND=S-tTMrXV@VKX zk8|wVAKeK%=a6E{w$RZ)zN-;4J(KXO_S?P(Y5};tL0wdaGwH;PH5>FE1Yd1j04cK9 z(bu-R%WZ1qy%D;c+y_(BF89BUr+>p;fXhBOgGh((X;_$=rdgf8xsgE-c>T<~lCl}26sXf#v zt!F1DcP1xmiU}r$Oq}CCKJs4V(>UEllH91omG@&=ZCrTd>t?%)pm&C+45xV;9nRN$ zetL1ZRU_(0<-?e^%8gt1|6r+7w>qYR(#(mJ@lUf{S(5V$Fr>A*faJ<+cds9qVz07F znCa}F?ws(mS!-D{GL*Byc=u7(0Y=7^-EDd;1;6!f$Ujy1CC!z0USjz@+qeLFY0|8| z<5*is_PbGna)zsZ1t)L}y1K1T#ZzlkVUZkwK30-={{GcC$Bg!pv}3uwPDC$o9AP9( z_|Y!vlkv{$eynGgzEB&Yhs&OfhOb@os292P`@Cq{?_cX(lHAHluX^-UnJHltXjJFu)MJ@s}3 zLZBB*lJ|I{7MAVqaWaiNSo?PWpc8;cbiyW}{tW4MC>WU#QD-x02Tgk0b9TQ^Qfl`O zOQ^`1xWzv-sfY6YJfsqqs_^i@Vj0p<)1=Sr;g2Ti9`c71kYb2H8(o|1FPjK1fTgc;mhHnTi46YFvytgroBh0e`weRGJH)E#(mXTGOo z5=kR>p{0(}utkIex7cP5x7gXg!cF=-2O-`!6oO-#n=dbwu7!+hW`|;K_=R>o%{#tG zUQzxJ;<`m%|C>wPvWcFFKKKCs^mFlf+xPQn`{_229_m3@EcOGqPg1|SQqL%2WiyrN z2%4u$Fr#&kSSD!KzXsk=g|m!%ca^>tB%?1Z-iRq%r=hAVLTa&wpJy(#1~M*ri`-$a zu}t3+b+|_C*9;`hr5BQ)vviD*J@+E0U3s*MSD#=%nP}0Evbm7d7+x>>Irkh+$cAp- z!xi7SM996(d%qq}H)W157+$9h6!0MIFp&<-t}nLo<(*?bUE{_xiImcg@wJGU@*u@B zA#a7S3`$Hm58Vh(*)Iz6K8J)H+rvXt?R;BL&J^nKhi*9$Ti2PytELTDiQ;K+LsaYE zRpfub{CkUovPK0`KYmd4go8(Tlyz_VJMr-|L=r!l&+@TVx@I&Oh(fN?X#OdG86avs8Bl(IAOYmty1T MY<+(^D4-Aj+4S=w(EtDd literal 0 HcmV?d00001 diff --git a/doc/Eqs/compute_fep_fep.tex b/doc/Eqs/compute_fep_fep.tex new file mode 100644 index 0000000000..718aad3c40 --- /dev/null +++ b/doc/Eqs/compute_fep_fep.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \Delta_0^1 A = \sum_{i=0}^{n-1} \Delta_{\lambda_i}^{\lambda_{i+1}} A = +- kT \sum_{i=0}^{n-1} \ln \left< \exp \left( - \frac{U(\lambda_{i+1}) - + U(\lambda_i)}{kT} \right) \right>_{\lambda_i} \] + +\end{document} diff --git a/doc/Eqs/compute_fep_lambda.jpg b/doc/Eqs/compute_fep_lambda.jpg new file mode 100644 index 0000000000000000000000000000000000000000..5ef9e8b9f2fbce24c23d751f23986e87f2a16445 GIT binary patch literal 10511 zcmbVx30#s}*Y5+)s5z#orB-U0DNcZzX^MzAp*W(I;e?3b00^0BrDkg8Y0|QjW|L)^ zl~bu{PFY!*LuQ&Oc*-UV8i)enKA!X5bKd*??)TmAeoK7#v-aBiS!?a}?ET*$n~=={ zn!esRZvX;;06yR!Amgb;;?U@rAOhYS=Z^s!06@*hpF&TCY61X_&deZSJxwEtQKm{y z04SgWC<1l>K#F6e1%!Bq0-)e9Xj2Agw1oc=;Wz+}1OTJfK0&6Y|LFf)NGmQag9!kT zAkf+&K7kPj;(QRNu$gH~dOnDCW2s9RD!+s?KnFp*VhNM~!W;jz`3rAZ!tpeEJZQ7z zb6PwtehK%1_&_Er0mO3tAl{!zNnnF`48&$BEE)yGA`t7+5=aaHkXKvMGZW&HKx_+Q zwTw^#8pN&upsYszHyrzKn3=!<{R9AXYTC{W3OR{sx<1a*)Xv%2$Xnd4Vx=%mmy#Nnnv%-OFlD5X z;u1`)|6>vVk30UGTmR=yZxIF zOYpC{27%6bDWDr;185HE0&)wF0C^o%KyGUl*aG=`-uzXKpx@;HIaN75xz%#ka!zt+IlNqyT%uftT#j6^T)Es? zxodK5aszUsa0RIpNTQNSrgDv%Y}3i}nx6)q|?EA%ToQ+TZ)R8&;dQ(UKrQuI+IDkdxLQaq@5 zTCqX#uHvxboZ@#SB_#tTE2Yg!cqNh&Q)$1_Nu{ewT}mTLua!i~s>&wH_R8MMQOb1X zeahv^b;_N}Bg*s2Viipla}^gAyh^;vPL(p1^D1pBLn^OT#4s(`I@o4dC@dMa7j^=6 z4b~5P3Hz$5s=7wiSv6RdqPj=*gz9zG`>I^kpK97_8`RKhTh&-L+4 zZlS(KJxZOaen|bYdawE`biE<3fXW!cEGPZ}y3<{BOv+cmN@$~77_ zhBQ8Es%TnhqBTjHIhv<5Z)-l+{H~>=Wv7MLqG=t}s?&O)^;TO++d>`8FXt>jwfxTVSv@&D z3q71(ie8!CO}%lwU;3-`J@gawi}bJQkLdqcVYFh)ii8!#D;icjTk*@l)Bs~ZH8^b0 zYA|gmZ@9rQ*pO{lW!P`{(MZ>5lTn;evC&PV$(7KR8&(ol?pk?n<)f9~R~fIuu1Z^V za#ioDkH&h&Ta1&9j~RCwzcbM>aWkQq95d-Md2hPh)WbBz^n_`jDS!3K)jq3Pt7}$2 zSuI|(ZcW&leQO%lOs|Elby}Oa_So8 zSQJ{cTD)DiVjXT>*19X}UanVP@4h~L{n_5rmQOc8Hy}17Z8)`I$O>wO zw4zv@wi@23u+e!VedF1U&#l$0J*+dWuUK|cq0CS_P`{&|JLx(FIURJm@2ueL>747_;r!DD>B4lm>GFA#^(N}3x=n9g*SRLR zo_C$wyk;|LbIs;iH&eGAZfD$P-B-Jl+|Ro6wyfO}zvbeVc@ImEWRI&JpFC|nGd!C; zf1q8^yU};OS^+L$m*CFYg)8gH`q6>mNkf!&3@>!aY~=X2QSIc^m$4tE*H z_eJ^c_U-di^9%8-^yB$&@XzpX3xEdr1{@7|8E76z4{XH)cpUyHemZDfPTHBS{6DLwmys%))TG~zBT-E_>Ty$h$9iRk?_dfk%L4- zB87M>N+~Kl>SEOQXiW6+=+|2jTla4r-?nZWXWN7AhTBuN--*$PA;mQAP}mW%qi%V8esYk5!tO6D{(=GEb!Ik~X z_Gj#WUbv~S`hffa%7G_E4n-%6q{Z>Y4@+!I%1a~%;|@M7wJSYQDm#>T=t&u}tm-$# z-{`-MA9g={>4?^mtRr(r1CF*FGd)&(?A!5};}6Om%d0D36|9Qc6aFV|oisc7+et}f zQsuK#o~IgqU-^5{?>|n*pB|~&Qgy9*Rdq@AuQQZ06E)bHma`UT%g-sE%RKkyeE9i+ z3r-ghk5fm33uTpjTK|-d){#^=Z9V{jF=(*J>K{8cMDM z*IC!!-`H_u{HEW{o<^s}Yfa`&zc=eN7q>uKcDC?alUiqQ5pNCO_PyQHwyCYT-KM>^ zV|B-=JIn8sb;3IHJ7ry2UElAf-Tl~2?w;$3>6z+{>>cY1?t9Yj*MI+>_r2Z$kAbfH zo9}l#aCvb1q0__GLF8b|BgCWT$B4(xPmoVqhEPMdo;p8m8+IM;9C07%9`zc%H-;M< zd=~g@csy);;`!F+vlHIxO>;JJYr2I)LmUsv_=AQzdU;gAJf4$2e*$*gzq$3&B{(c7X&**2MfA<_eBlkD9 zUK+zA1dYQjy?c0g`_Pj~DdB;!v7StCZ-3h?WL8!>i{U`Ck0qqh*bykIe^f9E7aDBq z0n+s_N@yV6+bb3wk9VYbVPQxV)_G@SMx+D5E;JI&V8aur^l*wRAK_kC)v){DlplD5|5?(A`=o}l(?u+ zCx;9Y+J_d9;fKtOb%!ECEAWE>^XHxTZ}grjNcK|3j_RDx|VfkEGy;^PfVw5eI3jvQhN zokmMRGm;pD1V02NFpZt!8-Y)9_V=f-Q?1xx6eJ}GpBx-w1-GS>!yMB|u=pf6gOx}m zrZ~`(nQ`$52VyWh081vJ@QwsKXAGUr%3>lp2?#neBrU-s!j@qd5*L((O{F431Cb6i zFBl6I=M_R_MfloA1(K1;H2W017soLX9TkpG4GOo#dj)xe!B8B7DQseBT4VqQ6-Fnp zQ1Xpwety};QZ24D6s+Qq|`Jb0UJ)S_07s~bh1K*pxI$glZ}gHW0+PRcvwb&uY;3kkQ15?_n;%met{$$%??LIQazmQ zQX>$y7$19&*mUn8TdbX}r-MBsva--w;mMw{ z8SJ2VD@;P7CppM59OINkp;}R#;7KWP4@zb#Inyydp6wA1_ldO%NXf);B4JJ#hqS1O z6atIFiKmhf{;{@cnIU1BA&krrPP}&}GCU{^ZI$AW49QH3uu4H8ZHbsTyNC$y0Kc@< zCe7d$LBM{0_5wSqC@Ls|+W$|H-37Fi!Ncgd9Apgu)q==r zL1cY^3AmRi{N>!z#;_z1DCigHkP1u{G-%cYpb$AZ&|L)udGLG-*$uV>@>&YotL;1# zb%IGsYtnV?_a3fMUh8?IdpTj4Z{`r2u}=l2r@z9$(A;9(ddm%t2qenM*#+%|@y7b# zd_zLR!Xvh1xApY)_1_z~|KQ=s=-9LI=Myg`xxBeQUcZ@t`|iEq%hzw;g+D|;e=WrY z?u7q4>Hj*!|A)A=z__6D@^bP@OL0M9yw#FZcC;=&RH?M(ivDhFwH5Kn5JB7T{&TG1j-3ZjDK$yE353_;~$? z9Qmh`)Y=#Ceyka13c7mXS|WRPhQo=P@r?^+C+#HZSI)TVR9Vg6mjOFY5S->@!2bIp z(Zq_EGukohWPs`OVRwZbSVK2$?bhMvyxP)^aQL?uUQf4* z`%8hGFj4wZ;d>dduR;cN`^y0G=i*LVL0ENf*}f`0KD(g9>LLe!udTJPzxmT`665mr z_gBXmp7&$`HL_Rjao2snxYx@mpCG?BNtIuV{j-A>8)U$2Wz5aoftgaa){r1I^y&PF z1e?3!;O@?^0e5bVzG>f3e5rmD(colon8&dK0J8OSNp51-Bz4w(p->zw9e2O!o+r`a zUG8)c;k`yXaOXKwp!Z6`z~&k(BQYVX{REO9?}WIDjLL{B(zO`kz~ z0Ek_R*Pqci;$|a#F{A9J!nv0V6^-_oEdSg*F?;BBEx+t;?n+Suesa##T6p}z%P9xJ zSJR^zGC*^=0M!o{Sz!xY6$E*+{olKKG>ZMimea)K78#%|32Tr(nbBfex?0*}<$vW| z-aP%OLj5dd!{KDj>BiQRMvuvG&HjwRANu`WFB04~ik_qzv@U1~LV7(G;+mxo`4tDF z14b(nbJCSdJ2R)huKZfiQ0iut+wGLIku%S8?;cu~RNc~bFFNMMQ@@?N1vV-<7O!kB z*Y^||PEzzftEJz$s?%|EFny=mgS4Wg)g{zz&HcBO-n;K}WzBXKb!zeF%cMr40bhaA zp5_v-t`XK9ji6#_&o3nd+>WX>4>s8T;i7%9eZv=gUbVbbUHU`{9hNT7RuV;UWq_i@ zesr+8Jdayytd8u_%iQ?sdQV;ZbWvh9J<C9Yr(mKZK) z@YNbo!o?4o_}x5sQH*Bu3Ss@XEXAUDg^Q=zWtH3PzlM%kk4Li~5msa#cSq!UAbw&6 zL&A{78drC43;=xyn_76th8g6QjV>1-< zxQpnmW2^L=km11rj5HbW5pC4foc&yECs7k!;F_$+j$f>CPr9=U-L+UF*)23O8gy5^ zI`93|k%n4OznC+E}3- zZDwr44{YWJc-gPCL%LjOZhlyM?u4+Fe>BE6w^s=x1F&U+&oW@yCK({8{B@MOuGfQq zs=K^X9dzeZU)9zxTUUkjx3wo{mHaF{U1}G6YN3$>y+mm-Uk1=VmvpIju*v7M zBl)>KF#?3pR)3|52pX)NZScnXef4Eqln-uecA><0y<>!*h3SO;Uyq+D*AMDfOF!~rA zC9hPiZPX(a#z5`;%7agf2!G)J$Uk{r0ao*}J;UvR$X%?O)7RBFbMTy~kgp+h5{1p? znk<%nlK~4u%GsMo9BJ75yW4qUOp~(MDE75O(}M9a$j>k^s?#DCxDp6U7B9Nb9-6rs ze(v04ZcneE;$F#}ocGdb{I^2>#lqUo8r~|Wtrq6RMm?4B_G_+dlThTOhBNLd8ZUH& zF`^G*&)jZAZi0I5?2kfxUiO+w8E|N{_rZmYhRmuJBh0ssx0x)T%=OJQzwP|*y-_QB z*HFaURz=XVh8Dua&Jxa87q#IFryGmr!XF!nhGQx#XBKFJIBtYQ_v_u58#DbMVpL4_$N)W8xm+GT-*EaE8<{mb-h`&JN{v6E zDkB?EQPb8Elve$<`@C|!;@B!y&he)ZjBXGFlS7xjjA=z3k^%7=2V!pO=R0=2xc8wi zM^$uA5Z61S`q`Dl;FWB4>Gi3IsN#GnpL^VPyUMY3=Jn5Duk5i!Y1p$|pG&~m;`QMF zmw?ncRIi4*WE;4|>+~6KEFR?zlrU-dKI4@m=EY$y1=mgpi?RiNtq*5(l97cEXWrPi zyIk2wxCvxU>jrO8(2e-xxkOh(cw_NWj=UsyF+WEx=h5@rWewRRLG3+#H=QycL3zpL zt<%J)7f}JbFMqImK-&p>tX|*bqh8}hF^*sS1p^in&UQI>Zpy|l-t2G|%nJ$NWK-|C zt6Ge^M%N^}RFwQ7&@VtlR6d#U^-JGfM?^0>Q_MHIvWR>dwdu2W2lne9p{$1CN?`rj zVqks4eRrLlXELD0q6Vz}v7q=l?8y28nM;W-;Nl!ZaNWH{%hAZw{gFdN2bk~-Y3p))ZBEo{2mdD z_&EDV;vT(XNiE1fs&d9>nrc6ubN@&pi=E!(EPIyiA;9zARPzg(a&_NU7K~z%=a2YQ z77x)_`p0Qxg$pkmSMLuoji2Oy-1KW^vYJ=6Fvx!%v{=|_n634^Q~$k*uA3?6NUEY} zAVi>%k0|>%h${5%7$ZNcr=1ydov1(D^nj#yC|8SfX== zQV0fVx8dGCwmNe7&M}(&q5}rV-5>*6s|PeDjfCAIhXin@iHns@Cmm;AV1+RPf0N}o zhEsQb&ushAC#JdOTJ^O`vnO_`tGyknL#JvQv))-d92mCF?;5qJ;B~>k>c?N?eC3Yc zHg2EI)e*4}G}YkY=J3`4@9|F%^NyAu>9+C2wTBHXJe6M>1Z4Tv)$OT+?!9|~Yg-3A z26E)FV$19uoZ<6}WjUL#=4ZHbxmBB;WWd8aIi=FR8TF1Z{!~vV>bfANXULEf{(e3L zM`{t&4p>up%pb}(%3fg@m!`LFuA@Kvxjs}I727#;c8~k%84+A#!BXs+Z7)!g=qPo& zYq@RWpwWWPN9bpnzSH0p4n%!`*Z*$SUdi6q}Ix7@h zVswL)UTZ9*^Vjk;$~x`0aSD5@8|VAowcnLp>^69oZ7z-m_vcT)Z)3}?7`Y0cE!diV zGBe@pgH6;gL&6e~I`2ewuGl@>VnhbSrIwb7LpX&YcgEb7Q}wG`O-jBu@sCe8pTn|v zn+iJGJNHjMd1Cc!Ke1~3bv$)~=30`Mb-n9*SZL)dIc7yE%;-YtVKb|*1?GNgzgAuO z2?O}mFOGIsn@CNvb@}V^x+pTBw36HxQ<{l<71%guy{?DCz16J$aUuSwZ;^$Y7<*$? zXF{=QrpB4KXZOG)s*9IgchBMrXZYLTFWh-b3o$&9#&OUfSuXoH&kI0vyNWwv>Z0F8 zF+_DgLL2kK_F1*>_v!dHvZhECi8e0_#qr?2UqrLc$irN%PyghP0BSs5i@+ z-l44Z3m3R;F-O=Vbn}vIb+ysmy96J4e^nHBF3ZO7g@?KIF_F(~z6~5whoc3hGX?NZ z)lF&dTW(?yr>cK07+ukb61uFHZ)(L?`xI;K=z7} zj!ir~R8-MhSr_xt=T}ULn`LsYCQCt023WP!=emAvyZ$pDBfOXfG+erLMq|ElHg}-w z#W`UlxE!3y?T&ZbAf2dgDg^nbKtE=zV=a~YSm$1)#E?AcYE_$*RuaA7uwZWZ-m+PB z!P`LZrBn2YD4Q6A4>{)9Xpxv7BgBYi#F=lAo%a0dKKBE;P51&yw8_2-?;E$qZL(3w zh8j`gbAPIzh`8`(%#rHTP+BA2{OrzavFDJ^fT?@i(Rbr0Hu58% zpB*zREZw`UcjZ&1CzGEgx_(@I9!Q~z40Fre3^{Y2qAqSdqxY4`Dek8l(hl%@jP3n~se=H_+6`BjDIIH!X7 z<>2NH?$G-??u^38*T>2s3Aijrv=t(;l9RqKa4Z*nTOa9 z)PynspWAIy-Pft#xY*c5j{dxIJGBZb0(T&(riS9+rMFqjD$-MTxNbh1tZq<(y)pVx zxOj!omN1oaZ8`tRVv-zqqL^){*65-Sc1^IQFh8FAGU-^C`qfS#x95}qGbjq2pM6rp zy0&VwBQ-BQx$XM%BdZ65HKPI-#kpZH$OC)oiKX8yc1`^%Lquj0%sqta~ z&n05No7#*hQSvgo-CVr2?faLM71_0ipK!k(WPBSc?a=3%6y>N3$h{2*jEx${T~&DM z$T_d^rczIZ%JE+#Jc~mdi_%-1S14wJtLDA7Uw~xkjJ)SVwMK_NxbB18dY`W(bn%>< z#k*H3i`59%4sa`2+nd)`Ed28%V%Pa98Nr|Bb+jFW! zYXv&J?k%W={OYEG9_!E#?v3ufL%@v4sHf9$lpelYqd%*qaW}>7st{h*@Aaw4H*?s<@yHCT_jo&v>u6|ebsclLxEKce@x7*`GcyJi>?0RMWJ)44*dccRU zzxvR27tv{Ph6Evc&MVV+KUvt@RaBm1FbvN|ao;hcGjH7HzbUIz;3VE|k6SZ%`Qg_`9c-HJK0>dQLi_x#J6mpz=OIO@z b{WYDzo1^u#9@i%YVW*$Hjpvl8A(83U_gIJqJdFx=t*fKEtF_HwjQ4G0WU6?hA91A+iQ zpbr4yktvC8-VQzhn4IlxRa3x1fAGH&eG&kl1OQ_?P9CbN|H}WrLK2aQ$*BOqQ3Yu$=&4i%HB#M#dsiRS!fSRMj^(H&bPjdrs{Zv zN20=$qf~7%=)~}Z3;_7M%ztVDl7ISE73^daeRC5N9Rppk`~R8#k2n8W>i-P>jP2h` zY+ynf^Zu{Ilf$4F2tXx_{pH&%RT&i;f9Ti%(Vk)2We| zcuZQdYD!{wWVEWzf1bqu>x%!@tbc3AVXx?z=;Y`G@Kt``EJG&5g2SB$~1 z|I-NnFRT4q8~(t*&ub7!-Q@t%VY-0$ur$E4_8Q=o5(apVmxFh>{yA>0f_}gs>3J z`uBMcV(|XoKL1}I+{NHe?i6IK>Yr>|FCW#&wB+;V@54)_3pKqwFiAOJLw3}68~a0SKiE_p5$E=?|NE(0zzE-Nm3E>|uuu0XC6 zT(MjUTxnc*t}|Q(T$i}YxbAR0;A-G{%GJa5f@_3pnrne;nd=AFZ*CrL5pHR2CGP#) z5NZKf=Gnza=0bATOXTU?~6>2p32d$Pu_M@JN6x zFe>m_fU!$>m&z`KT@Jf~b|vgOy{lx`!(H9GMt6PP#S|15)D%1-2p5bJ%n&RVyerr) zI4t;CkSQb~q$Ol2%k1 z6gebfD{@>UO{7TVp2#ziX^~A)QPKUP$3%lfQ$>qJABgse&WSR1OYPR(?Yui`H*xok z-7ULEcdv^HifM{ji-n41ij{~piVcgciVKSG7q=A;7bl3{5PvE@CB7vgC7~|?mq1Hg zka#HZLgJgGfaHEjd&wxtvyxSkeUeL3JW}dXwo;K&XQb{*4M=^K=9kuzc9xElE|9L1 zek)Ctk(4o#@sq*H+>q&#nV02}-7o7b8!uZd`$Tq9_P3mpoV8rE+9~cR{4(#yb6aDJQc7Cc&g|vh zduXrM-mJYZigLH|vWk?7l?qbjiV9g}MO8-C zS~Xtvnrgo)b>H57PW#gK-P!kcA5%?B%~$QT8cFS=x{$h=dW`xN^hX)%tKi^Z@ig(t*kY;|KW4G$U=J zXrpqY_r_AjZpOLBy~b=4Q0L!!Jm&CAI~{H8KM<}3waT$ z5E>ua6($xI9@cn*?}Yz}hbLI!@bJp;tqA9cn-SDV+sM+$?@`C1u0$dm#=aY^n@1GJng*x@-wBG4U zr+=RDKhu6z>Fmj~OXnQV)#mKZNzR$dJ(^pQ$D4=DdwbsS{Ppvk{HXkw1$qS~1*{8^ z7hV?X7hWseDT*n2TWnHX{ulpW34cvqgkHRVN#auGrKQVmms_r=Udg}m^J>`D7bQj| z6{SL@X{GbmT(7lV*SP-IbygXoY~qH^4bsiMH_zYPz7=(AwES3keT7m*LB;Re$lLGl zINoWg++SHz#b1?P_2sVL-Jxo;>IXFnH3c>7dkOdE?|a?ve_;CH!Na`|i)*=S(`uI= z9e?z$&aSSlUZ?&JNtRUb7zO`A!dVa}fX!1p2lqxi>? zxxI6hl!Fw~yvcmmg5ARFMeoJgrO2i4pHe=tKA-&}`laNn%GU?q48Ct9d5&HW!Wxt4D8{09b%|2)Im+t%6n&$qR;LwrD7c!Zx;i*SddeUOoXf$o8NIGX^2L^}iL@IYK*oW6B*Tqf2xIws29DFEVS6BA=+12;=^ z6mm#)Get*c7#n6L7$!J*ctn|*+Pj%1qxI}%k$w&lI7FOba-x19+9Wv!nWX0( z@002SaY?q1%Jgv#5Q4ZP{Pl3jF&^G1h#NXJ!T}v%n~E~iHbE!+d1Rt-OgP*xGcm^0 zCmCXp=C7S(;t`N&0P%1&F}1f(L+J|{`dG)s#KDtIOw*mxT>_kZG6T~PDJ}`#hNcM+ zSQ6aHKRVjkAO&TdnUP`^9}uAL9^vP1jElt?BLnm!+p5`9z zKK?NgXtZB|A=1m)J1_$oDK16(j@_xOmQ05?>uUbv8%et<(t zM3R3>l0gbO0+D1A6d08m6>INk=osbY;AIFmPPdMC!-o4|TyhD{h!)a|M?~udpiwq9M$QfnfpB9-8ymj_Z|_78gA7!%Hx3;i znPC764A+m-%Lp)bGC;-0I~n=fczLGB;{5f};)P87ZBuOAkg!<)gmCwCn2Tp@0uE+} z^hpWVbN3H$%pQ@f-{FFkXd zJu*2d!7RqjDFfr;8srN}$3^P7X1YZsxo2qOl9J;+qusC>CVnQ6C<8leMyegw)?M34 zD8=5%$i*bX+$$h12!(bt@rgsHpi}+z>>~W^B4gssBF*9cNI$=1WAo%dZF?`hbX>G^ zifL>*+9T6QKgA0rl;PuK80qQ}=w_a2fJ^o9*SGaf2=ept2?&Q_6QbQ?P23~=Gb7P~ z$=ZQIsR&n7KRdkuLl;9F0v#C_X^wLhO7TgsbqvRP8)70d!vpoa6U<`6y)drU3BG{= zsfa+dv0jP+F2L9`EiNI`Mc)t|W$bOA=ntw&stYm=m2M;C=^U75tZ$g)=c4E9VV~^p z9F>{qh%)hV@is9@HFWehGYjyCnIRJ3E-+7&afEw-u?Ng6#wW<$Fg^utZwePeI=Q>X z8>A;dGBE)$F2-pv-!vZw##Jh)Cyf z|8P$~gpUElF3!j!AT>P-5-DVhMko85q@;P7xSOF9aNdr_Uj7F9c82LGHtxx883}0b zc({+h9>&APARcWGiS^ZXN%C}!GmLdJPl7pR*a;ciBamqxUYW6;Nf<DYvHtVaUY+R4npT-zpAJJvHAYZC;q5psZ7$9p)#(v2Kb zjqKbZ)~OKdD2TN+1ncEt*l<1X|7?70c z@1NvlkmLnV@=Y^w_V9CwHFwqz_scL5a`D!8hUvRR8YEi7v~hm6o=Nd&I|MFVFD@No z9qE>YO^>w{0(NEr+dmPle;0`3SW%Flj~~qa|Cx540TR0aW3DA0E;WE#f{RCjYo{Mj z0lgI8-y8SG<@`xp++e%F1_=rYg9Vz!0d6iH9A6(K$Mn%WOB9L(@scGq0Tt?=Zv*&Vh^UmjAx_sqoN$IugWtCNTt84DvfAH{0 zV^ecWYunTI-oE~U!J+3bUXG59PfSj|pPpG*T>A9+%hzwqE3_Y*Key=Hj9JTd#+BIo+zdD5#{Q6d0J9!>cfLn>+u&->*)Ah2k}R=23hy zt#lwPX9p1IHf6;2cUw{|e~np$+(iU^kSi^-9Q>s=og}G$!0z#|iaNJbG@LB;kU?Zg zkI`#X8XQ--n8yj@iE;Fj(0$a>QyUly%cLy1>j`NY-mAZT5}qnv-T2yEth7CqPk2qF zx(?^6?Aie$c7U@x0N-j%I~BUdO%VSE743|s9bH(NMG_7^%^$HJ_+gEwxlpq!S5RM& zm$$zq1O-$VAr{K?go%%H*Dh)m;UUaeygH+U<^b7?N3hGSRO8AeXfdRPT7+>n%zw;B zk-dNIQR;nu%*;#QrZ#ZS_;E%acjq5)m~hz^V3WHAD~)m&$b+M|V|nNp#%VaGEN=TO zG#oO$vGBF1X?PFb@Exhs@OCikApDFW19q&7DVv*C*?07KK<;_D%wfco!s$MvWOcrA z-PVm5hvFLI`wn{gMJ1Kq_U=hVILj|+Y6sBt5U9XaElv$?h!T5jy7^g>PidyP>sDNh zR}1&@E!_A^#d2fM_&0TrtT*lQc!S?|zwEH&-?mS3PV$CBP-yLT2tI`-M|a)<&YfZU z;FZ}Ar|9Qt>xGMAe2CU=rLj)^yN;CvjQ@*pB zV;QRUex%|@@r1*#AKop7F)C<=&xrip$~em6&;Ud(5CPqdH?MJf^u6ru9j#JyELupe z#1V7sVfL`~8v+uaPz0GFbA*UYGs3Wy54J+68$gh$T`Y`z{v1xFKj`Gs(awW$ztG=k zcJ1`4!cNPsGhb_>c7W3l@IE73b*6MQhzS8K9V+nx;Q(QzT)VXINX%uLuBa8^b({Rd*zThpyJOmW4BsyvEVe~d5$u&R9SnJqlP5N zD;r@%8Ki|T_f(mKQa7AP6>cEo9j95QMtK*$cyfO08mQl9BlIznfjhyKv=hXYU^Ki|* zXR|peHkU}#DpZ(G1m=A!XBT!}Y$j`|d1<9vr;{q%$h60;aCRkO9}L$v59i(eKpsl@ zbljf*NQr$Az_wuDgrbU15}Su|JM9-YPAcn?Cp#h4A-AkHy`NGiYpa6_&SppkL|*!_ z%P%nE(n0m>>WAO8ul}WuZ+>piOk;7Mq5IKt*Ba~JELuY8Q6r0Ol_CgjtZG({y>}yg%Exvy=G!LB(?g(d+hl^N1xw!3>NJvQ*h`VKPiu3g0tzHPot~}&UXaw z0E(=mR?2Xh<+^z%{$_A#ydmD^{F70M`T2(0T6SI#dnG&~P-#T5g$gOMP@$RjD2p?$ zQn&j{GKWrf+E&kg&)iSC_gb^LtFf&x<}~hR;`47SDr@cp|Ub1xhd zm?kz3t?i?3)2~xE`Yo}~B7O*ygmB-38Q4W7LvN?5t|#M71=BkF10_upC8M0`7k)jV zPnrA>@1Pgo`Tir=;Sy##j3e}7QB34|IphqbS?ug=zaMw-`5A4ZA|qx_JF9KUt=!9! za~iEV+XY&dvxEiurMDBm$Bywyd;arMk>^mzN*s00Yn2AlnjF&>ulwZPS6c3AygG65 zek5(L!JA0cC#{!0SL)jzhG<;Q2#YQBvtxgH{^8sqd@Y^8zHepDD5jrbS8;e*QKJ^> z_i;CR=7io^xb40^uW#@QT^lDzG~NMn&wX6|F2kai&=8y1r06{T6?(BwSNrShzp?ac z#zkt%{Ko1pTFT}mT9hvH0Q500v%Jk#Bfi{{BU}RAWFK_X9F$(5M(^dVMw+4RC=53;MtI-j|hiaZX z3?|D(B>lJmWV6NA+-U7#>Tf^`gkd3zvko<6V-_}El&=*_q|=96P%pbxk?MUEs-McV zx5t=;8|hc*eum-F)8>%gyQ_QeH`@12 z7)^b?v)!>E6@?1Uv$60$a_-@An|E(g;#N*g43!mCJpfc%nmp|RY0rT6$%bkM)@h>C zx_-rD`df*~a8_1E+Mxjv302)6M_XUse|WdV61XiU(#*bVq4bb2QLf6q*i<3*9UFRd zgvE!Z2^^o?*Id92k>o+2VX z9;L%*S{Itzb^t`y;HgKQ#+Z3G!g_F9?2q1$)`v}sr6&<%YH!kuCaHR9Wll3%!kf7) zNsJAdQAn*_99r7}mP8d`VJe)_(8I*@eg$brUVp!CIj2iQy(L8>B_HG*TAMne52t?! z`D4Fvza*lE9$P&?>C6EW74>Cw81=!Q&)t*MqcKP2aR_xv6^6lmdgDAf3U3sbN0sPew# z=pTf4H5B4ai-&8el>NqAL^rfJhl*&RfL)4byoP}NG^7?ulcznM=k)O}>R zVspk9?K7tiE2~afxJ5#;=~-eQ>J2%9*%8L@vnowm19dKev9zH=B0?qaNKRL_#VAbU zt1C?t)SA?vzlsIJuwIpJLA+0G~a zeP-5d?qEi{cCpe*Id_P#UvPoteu`hVyPJvqm`32Ia?Kp=inh&r)6?bqHr1SkO)SQr z3n1f^viv5twCk)aU9?F&csW{Z!OtznOHQXP=dMR4iKOtK zJAeMeky>?wbE#UJr5wQwCV^!*NsOtO{<<*mwO6IcgK^JmyuN9?y_+Gp1X*oUUh-?p zH#Dhf5sluf-DUc6llMH2e4vTdJF(e1f1j~b9f;SY@eM{@YA_7@w4 z3qA)lE{9dL`?F+(=^-@JK4KwRx>G%pCb@l#k#cvrTZ>j$y#w@;BydEJ#u3t|%L%nI zEww1bc1c6<%-l!vwB6Vqbo7s^62JU|ndI3adOqV675Z!k5MuFAgBQAr^Fhsl7g!nQ zE>xV3H*PH4{q{>1?8a=Dqi~R><%Yt}sBm>3 zA@o+LSZM{|zI>&pGfrDcFv139j~qq5x&O_%a`{MkS*iGS4d1d|#`+1q&O(3n-|aY9 za!l+!TJHD=3s!}+(xlQ!sQWkqXYS~%@OQXT3&obcNJFGwST?!7ioX{ z4xm8nvFC{3R0g`Ws4;cal%=)F+Pf<$%UC%D)76P3wpVZLX~*;BbL+FPOY#ec&s{>? z8hKY+W$@UD>o-@}9?m;r>(FWkQx|VT#r9Sdb{kGM4d;cbw=n&4nr2maP`^9A+q>Sl z(||haT(bU|*L4Fem~l~F=`Zan(=;j%{WcY{wr>Xz^rXU1an!$2-Y@c`>;S?%3;yRV z_C#;8K32qXCK_9q?iQt#Pa8kB9m$w$H^@c=wdF?e)zq-!>8WGwBMKN^&RZg|g;5@O zI6K_0umj|8@E40VegDqBQ8V}aI)~{Y@D1C)F$eLYN9HlWek+Kpd zYXQF(idu`T?%R9*F4C`{c}vN9dfYaC8;(JWD}E_K6<^w)FZ>kEAyPX_Dx`OS`6`OE zg?mdu(p{DsBRqEg)={tKrynlHb!&7e)HH`Do@6!JM^`djK3mI6tO#W~ACFx{$CPWZ z9~0+miBiqi_dlhDkOq{*7MgF4zFpU8LYwwxTGgUZl3(LgyJ`FlNzYzn4ZVQsz7uSVC7J-;ZVaCs$*$_uza4~Y^rE)hsR<1@4yz6^EtO$k9#*g?#%Z!&U!Jje zAwqe2^%DG2cMj>RI!7pj>4`UDmxJxT8%Bli0L9886UN#UIlRdPbU~Q$YyU-FSQU=g zQ?6e|ac{WMFZX7kV?Rl@0*gl7`k`T(yyg?~hRqd*>()6s*ey?WEt9R&dHWzb<$%6yq%+D;v4sSYPGBKu22 zC1@sR>VmRMy+_l8vx~yp3Q|Ozd0VzUUS1e+L#JRY+-Wb1-YfHf{!(U%JR`OQ`k*(v z&(tkbB(0PK5x)mE<64|$${*ZYp}9_$w&NeJed+r;O$oA^FS;D`(j*@7kz+OzUAnNr zlFb@y=RYOdlqokLHvN{;U&cBpIiMbAwRe&;fJsbxU93aOvnWlM_j%lM{Nl+ra;r}m z^$oE(cNHXQd|YF9obZRs-Z2De5eup(W36eLubuCH9M*0}!=U0d*Y0$q|61{XQ+&M; zAhdegO9SA=#V7@964?)+XwVz*wKFny0N(daBO9Q_RuROdhZT046$Csk;b>61OZ9eu z^HH95MLWQZLemQ)ljpwpZ>j76M~xJFMX?c;=~;RnLz9W(yr>W*BEeVA-+WYzL$*h<;wmu6|Q^rXX{4xy&`Fy@k8yl6V=Eg^EJFI!*3bIoGI_ zGNago5FaE*KIgC!F6<1*czeMV;oh$USB zNuWd(yNDQ#;awfmJq${0C4o2N4A6EN#It8UWE^af6~fkM^iHjO1c*=-YNA-4+#p$u zJYP;}NWR_in6bo!GaP%%4~$AeOoDH5k8Ut+Judn)FIsk8?no8BIrUR4>@8`{r8G>1 zIKQ;P*bndBg}X!yqc!xB!5gD`oSmIRdgMEvkPt!^vB%en2k*(g z2c5qOPIc(B;xh`(AIbfokPO)$6sOjvXt4)QXWkw`$)?UKtqe};&Q8T+b*=Z@7BdAk z!j%E*&)j~dvWGKGku>Tkz!VUhF!^5@FYX7;8NrikmQ6hdFbi*tZ>hr>^ml8i{i*Sb zDM_13)1*o$a`^pHZ$(pSAvh%qS}5Wy`+0H^SvW20jdu@0kNWaGEG@2dk`#SE2!_eV zB%zI)UyD3k8QJj5*D73!{uo-zG+`xD1;9WelqJo+VMmYeqg%hlh56J-CBt&q)Leg1PguHLGRKfZaW~ z`q|`W{K4%T>Fau2o7+7b?-l2V`!E8W5e2y-$QCBA+>Ft)w`2#9wLmV}#?1`ptD>-t z`J<7sqMdqyJt*zjJ``FSG-#^=Hx7@IOY!<(H^nego^cczO4Qb&u%_*PiV|m-C^8Ex z?NJfKJ114nESrojizzNcvUDpVQE3mdFZA))%6u5@>)sPnVtz0G;N@>Bj2LnO^e2HR zy8}=|=E)q-sT+8AYA{QNx<$(8=n;F|@!1PRkzwNQs~F;zuPlev$|Au_ga z)L9Sqyz0Q;R=&cuLTsU|eiT?EGWWBH>>I(sA=>`5*qn7EwpJIXV``OJQfGC{55aYQ`isT&p0MG-t}4?H0v#EQ+0DSuPQ|L5A0@ zi3;5{v06F)voO*L&J!9KI_q+3u}pAjBv7+(emZ+rG;!Y9T!U25xcSBdvlssWb3k1Y7b)#1N$W-ilr(u?5`>zi9JU+ zJdCAz;_6!3eSA3eW6ecSvlg`qnkx#R;!Up<&$hWieWxH%-6*jpb%W#CIUm`VM5M7~(38p%zp*%=?U?WAA+oAS)(j-IVsMUoa>E!d!5Jl((QaL78T@EOk(yx; zv~f4vTW=PI-wS%x$)~+}biY#f@%j4#FDX921Q#S^! zlp1J$=Wx^}H_Ka}1d|dziyas=_dk@OB#LBtFbd}>XUL+2efSVYVO`A)>SphZCM9oc z&E>>^&f&FvsDkssdl%FSXNz4J>KrhtPW?Ur-3^_;RngdWub@*=<=lobBMqV)z%byu zsz$BLdHNs(C41!1qr9Tiy^|baw+pq8pZW0l`T{C76Tgt4cQa!*St;Q8*`?$-wqh^2 z#WB}vFJZiVFC#l;@r~%L*T}u`_yh?BH_HSa$SA^3aW=2yjm5W~(zj9P&d$mcy}tj7 zrs-a!LFr-a3b3QQR2oTx#iw=v84DCGcggVr9TQdga{6 zOsi{Zp^r}IDGaREN9De9lK9KWYw$JK?^`Mtb^sJe5-C)t4KT7IPvB=cTy|kMH8US-Rt$`^t65=+jl4&Qtfeizd<+4u2U%s9deXd`(o zaDK2gL~$rox^b$yspYAhU}T!ciI5pNm5jA@KNNNcNZ3z$1wRFq+X3RfZ@h2h2v#%Y z2(QEV@M#NS7cwcmO6u;kul*!NJajxY1hP;Ch1D~WcxTdi$5PVt9Lj#&Bq z_MjuIMwV5m&X`jKOLk5tiWvt+EG*Yq2bau=v0?&@w@@XP94$9*U&#`@bHw;t_e5Ha zZB|a8R>Opp$0jf7t66)IR~!DFz_d!!6ieEhZo@8SMc%_h8EZ5H&eTw;vQovM0it{_ zxWZU0U@9rkSxdKHT~!FF8=Ica==kgShh3HF&c1;c;H}eg^gHYd-EK*o)Y4=z4Qn?+ z5XDvajW$8V7?UYU>~mNA^jx!bh@b=^xA8^1m^v~f-64BU<`1C+z4N*rFqkD z(qaqAF~c+dPK<-|H0rj~(p6;{%YiK*=GG;IC?y20gm6K1IAa$O_-K zf!Cq#ldSJltyL&(y^l_&LW;NG42|ucVo}07lR4AJQ=QICM~34-I)$1S8mRffKd5f& zUQUcCmcJ`2q17*IP7V?J=?%MD_f0()d;f=7>ok$cDe*^tIpvr-9I-y7k!)d-03O z0-gaN5#$XSCsX2ia7`AHTWZ?v&{`g{AE zt}8Pa1_RK&$1WL^vbQE49VaUFAKb1!_P+cuxO9jia;+$vjIg4a)(k_~q=oT=INPjD>HaG;~~f%W2~_f*^@s)GVBj$b+$ zwfyzr-oN^%INBZdso8x@wYkL?!5BG(!q(Rvr$}h_wQe)e5`i%Qq{?g%C4l;+t7?{^ z=sUvVE-_@}XtO15>4f=94PZXm(Pyrdv`<`YKejpWnHa0~a(~g61D(Q4UG>$}8yq1f zQyia0t8c)jQ11;@h~k~8hPJJxuY#4t`im_|dEplWZz}yR%qh+iRw~?FZh5|IGeA#Z z<;%sp$oAc()!#BrZt>L=MkkcCl$4Ad_UMs3;A3aM;Olz~NagP4rxmXXCS`!e7CW$U zdIxBp8i1VJWVxV%hm{cByRDR;J|=fJH|Gyp+EAEqcQC}ewz^ig_Hpf_#He(3fx)kd z-|At9P~^sq{u%W5WtG*RX4M7F zX)lSC&}W)+TJMLx5lJQuqf#Phj|PRwS}XsRmw_BfWQrEcDIQ*=aD+QSgZ}aeK-<_0 zT48-?3`vSG6ea?VpzI>XGYp>*c1;;o$S_R%LlrK)=(Mf+ekA&LoPONJpvD*Rqj9K7zK-DIr6=bIyd^^C8 zqT>I;Fy9GG$!xZ+wo)B7=&20(dD0nd_x|F5w$Y%q3eTd~GmprKj>p-Tk~aE7@7HOV9+E7}ib^_fk+wu)9BA#YlX^Czb77{w;nB(n zL-y@p?8$%oI-L64GV)Q<<5K@;!M9Vk7YwGF{@c+!Y1KwL z*R9X#UmBvQi+R-Yjz!415xm40 zUL}j>*spxBf$3M9{pHAt3c9&?o0JNDf`{rfcgnW3<6}Li)_JN2`fQW7?){g!_dm54 zzB)CJkzxh1n~8BMv)DlbU)P9*L77r+4<<+Ay8^x?vygtZCgk|sN?GgG{mOeF#@gh@ z-lBpp)^~$H9>moz8gJcOGX;H`BE1eguVTu1LzJ9^GpzC01r$X%&a3xg6MZ>N*#2u@ zr@{HE7|AN}#BYT&k2^J~>Wk2vPRFY6?X7FMH0{u_x|+@XBU@Pzq3T=jIG^g!cWq55 z+Zqnrr0Q=x^I?qrt!siyVKeG<7piV8?KBR)rZUfbMb4>^K`)dYv>-`-yWD;20d&3F z7k2&xGs;$&S#Up?CoOv`>=Kmfc3zjDiH`-%(KW&ZN3p$pcAnTTcA>D60d@5+T-^xk z^E2V>9p7rZuEasTVp}az3iIDBw~!j~^&7uG{(b)#7q)hg3h4`L`ntMB8>1)EifXgN z7ceR~TTd#XD!b-L_2(wj$%56qUtvqRUn4!ZoV0`bTG^rGW z92`9-xx*Fz}B?e@gju~n+ z4%2T*dvMwRxnyV+Ye`IZye<10alzv|M}d9KBAll9OkuDwtp-;^6f_S1@PpBM6_5}&*}q;~n3$}Q;QigW7(U1CopdA@<%Tyy(foRu841Lr@l zb-LN^#4w7kV`2#pZCrjPH`Vfpvc|I<1{zt>?gK0n#;f@*#YO*~jl6c10xP8z9o4Zd z@Yc$^xXiTStLl9R@)uADHF@LC@B^E&!VgY+Ixhxa?i#T% z3AE-x{v^E;xVvox@bm100g{c8j0LMq`h4s1A)`8ew6{#;wZ+j`6cK;LW@cS@>JW6K3 zip00FTB+736FC(}ciNvaBRlUixN^`>Gr=s?V+X`Qu?U!|lD^+8sz68sn)bOrY9PAR4@ zXCkcGah1rlW59X|nvAgpwty=QuWZV|rYz<(bdH3VjgB(mIAcXsxz$#_pvmZ~7UO}o z51THU2@Hbd!@lA?S-#tZFbSmwhvjihsp+K)!?}t0)JCdB(Ei-asUsZ%rIUuv;7-JZ@Z(W7;lT zJ~?BH^AGKK+Lbf+($B0T*wRlYVPIYTb=0#P&U;9Yjfsr?&|Gksr&W5O4Pm{-MWF|% zQ@yjp(pDX`tdPy1?*l~f6CD}rY1itvd~ww+Psi)O__uYO#fbkZp*}kB;&Y}HrzcdN zTD(@rH04Y|dA7Q=dfFjp2r{AI@>t-^;ZEcBF+b||4Zg`@6k=ppI*9mQ_fER2wH~fs zGw*Pi_DQjKWd|xxLN%cC_h{rbo_fMd(29LL4AW4N#~(K)<=s$yiddvN=4zbrn!FSk zp88{wKEE7fwRbIbBKp^Hbs=`bf@3oQ#_4bO9bOY=Mshw>w6^9oRT>q9M3ZC5=PrGi zcDOWDiAz}YnOs*(OV>r<(Y!EE(i#E)T(7eeZt`4_l0#{EB$SQ20?i&A8~ zG2Iu+zRod3DyxrKnc>B!#QN53;k3KIvlvBa={}{691@8$WIJG_@!zd+-D;00S^|vQwFHpJ$qQ0b7It*+PW2QMrQH|a&i-fzHk3f z^C@hyEyMwG;qO0K6;%7;Std4~^EQnA@p#4RIc7Go=NNRp ziriY7W1&;W=?RkocL*@=i3^|4O>*S@)1X3tOlZXeLKfOI;qLKg4M6uk#Ni5GE%cn*r7oZSWkUo0`%0?QAjWs*Td z)gNna;n#&iI!l6jpC@>tFPWpG3SM1txpY!&@(?(KErb_}SEs=fPg6yN!+0kKX2E&Y zB6umpt+`nIg>GXumbX-Q;4^rhrv`_%7&`h%c3JZILg2Q+17&rP&MUERvO<{dgy$4V z3wdfwzzN0ngiIH<%vJZX%ZTCkHm-nis4l^}0n9WD7Q?!FHGSgWZfPxte! z4*OpYvgDxqKxO`ce_o^)6vm;i{ZMg6#r!<`Bu5Arv=qdyx3co7UDNF}D`l z*3cvCEXVsRdVSh~v&fC4sO1I)_4bj~5KXDIX?os_$)@Kbu(`p| zyf+9{B)o$@QOUJBj6VUcWx-Z{4) znDwxGw^FjwQW6)qE1Rl4J!O2d<^FjB?{BB^2-%=kx{?v_J%nNC6KEmEN}Mt~#B{;U zafTPLy@-45`6`C}Gppb4E&nK7I8)vDdTO+OlKtl9kctlBwEw4)rxq2>jx3qWeO6Mf zPcsM-gjd}%%KIn0j-D?OE>^^q%mfGTxn&ZMZFonR)mMBGwl*6xqgQuKC6n`-4APiW z#AwL$_jwXHFGsb)xN&lQvIM!YP#^m;#9DYj=W;rqx6z{-|9Je{^{lB*zwFOz<+ozf zi1$Mr`7TIYuP*Z!+#6S=d957a=^}u~F?uYm%y7az#AeKz8x^`RcQLz$GenW#1$Q93 z`B1It6;bcDV5v-Wm46+L{4+2jKEBU= zfmjQn#m+G5*Jmo?TGX_SV!T)tc#uwcGJ+=|CT-{l%Xnp*7-KP(SQ(hMw z3h#YBzgM5P^5o%JoMF%Ju!2r|8h2lBW|Wo1_)jL<)Ms+xasE-}E0kY3EMWgl(I56w z$3GgVOWq%Q=_9&U4xV5C54GXG+AkhzZ&^LAtsy2KC^6`JCXF}K|5-(2#j58L{4|-r z)0tWu#;$HIsI4U{$8pRQzMlPwGZKFBX?#PsS(x1Xiu2hxzk?wYm7{sl4q#-Y4#gzX?)YGSKM_n3P z*yAR&rs6DZ^*`(Zw_d^3>?+)zw})K*@iz+p@wW>9-FKCpudeSg%_mMu zh{}`ZBss?a6RH4J|5w7^JMg!Od<)~R4C(sUf_0rfZ7W&P^=mlqEN|^6Mv7=BfXqJTVa;IHiS;h%s%3j7oBcSrHpi}kHPL9_cJYZ}(RMx}d} eF4J8-x_\lambda \mathrm{d}\lambda +\approx \sum_{i=0}^{n-1} w_i \left< \frac{U(\lambda_{i} + \delta) - + U(\lambda_i)}{\delta} \right>_{\lambda_i} \] + +\end{document} diff --git a/doc/Eqs/compute_fep_u.jpg b/doc/Eqs/compute_fep_u.jpg new file mode 100644 index 0000000000000000000000000000000000000000..62df5dd0c03a6d20cca157cbc46053adb77ae90a GIT binary patch literal 9337 zcmbVw30P8FyZ;6h6g6kf$~1E-Q=9-b(;NU%5oeT2LqJ6Y6hUxE8cb6w8@05wY_!SB z95c<;FQ>)l+)dw^WDz5_j&I9-~adW?6rTq>s@QV(_ZUcd;ax&AE4%q zC*lDJ1Oj-0KVW`9IgIGx5$PXD#uI&UU=*ESzeHcmhBH zMF0-i0051ilt2o?2Lm7xaUO>>X!tk(|Af@(348$nK>R^z zI|eg}4&qD@$BP6B3w$YvwW8Py7%I1b`JjRzUc7)~{=#eil=%y*7cl9uAhrgvGCw%b z1H{e%pr9P{4;=LmEMSU3JpsUjmyp6|#l#8>&FQNQZ5$mP48545c&0#L=})7xX?%vE z2al6LUp6m{0yGwUYX~|SW8;XySlU{F?*C2yYv*sN{~avE_AiNV0e{8}qSO92 z@9(jH^LS+d;P3HjJ4Tk?Mf|9GC&!t;Ln&d`$?O%uio3>TbA=f(4ce8Z#!8l7oq`QMZH z-yZl6wf>>Unm}eWlh5RWj|v5|jKz%s!_8%|1S}rckj4F$8Sn~t3-kdWfDu3nOajy3 zLWY2-Kr|tG5Cez_!~$Xqae%l$a1dWeAS4{J84?5GLWGcX$PP#z2;PAWGiuOh!p-a_6sM{0I3-I2^76H-ls0Uhr^u96Sxa8-5&K0ly9JfDgidAP@*W zgau+9f{dUc1c)reQN$%g6XH4I145>tq+p<6tAJOaDsUCHD-p+-~7P%Boe zQ|nUup{}WJqfS=msP9(4p#DJpvj#%LR0F5M(8$y{rO~1>s0q_tsp+9f*W96bTJx^v z2Q9dknHEtiPAgCAvepwVskVl;y>_U!Si4yJmUf>GOvhA*s1vV~uXA0eQ|FhizOI`t zQ#VKVitcmWsl`hduV2huoV&PU@vFtZ^bGZIdThP@dNq3Qm&h$yy(D0XXi3SEyGurw zYAs#6l)f}~>Gh@E%b?3vFAH3jw(Qih_GLfxm+KSs6ZDVjx9E>9*IB-PdED|t%Nv&u z8E6`~7_bZu88jIT8)_T68O9qPF>E!Iu2{ChYlU#d$rVplOdFXQg&1u&sxW%L61mc0 zW%SBJEAOn78XFjsjMI%T8h4v0nmCxmniQI}nM|3QnNm!%O>0a)n=LjYnx&duG<#>R zV(x05XkKRiaus})!z%Wwj< zmTs2GmKQDit#qt>t+rd$Sbaemqo}C;s5aD`HQGAf`n2_18x0$8o9#CBHeYR5+tO`| zZC~1{*x~IYcC~gB_7?U``x5)tXiYQ;osGVOp2c7>e9RTh5Y`yG8G8)d<)G!@@37n9 zzN5UOyQ9Rh!SSaP#!29G-D!NSjO`Pdg8;Gg?PmcXC~yi=oSAmlH01 zt}9$=u4S$R>sPL4tUtT{liMn{IJZk~U)-(T`R-NjQyxwpTRd)i!aNC{xt>pO8n_T# z5v~Vsgpa{r#7hZiLK@+=m%Nvc*M6@qqCSyMEGJ66vEEy}TYZ#$f_#d627Fih@_p+` zP?9(4AnBc-i67Umh76F2#0P|Dyy66MZpJUd=9E=%?b&V~E9c6j2idYkIUU8*yQ*1K(9D6>V5?{el;B4m9 zaW%MXZYys&Pt5B`ut>;C=u31;Je(-y`|!^uL6SBl)e5x0VyazeF5D^XPj*QzPL_#6 zMU`T8F<0E4vN|OvHS;Www%m>WJG1$k*t(tN1em&?d~ zm}i|=kT|PN%l`;edhzux0Yke%P%au zkbe<+QFw9a(#A{AE_+_Cy<&OgWQ9&e-c{hL@apij&DT1w`&_?M=}>v)hRKa%Rhm_~ z)sX6xYH3YuO3>!?~mJx$E=h7oIQfy(GST^vds5M`uXq>#mJmeXkj>Kfj58Gtr&g zJ^gm;JNb9H@73NH^epQs>s{4b(TC}~)$iHgJ`gnUc91?e@<-AiGaoWPs(dW?Wbmo{ zv+d`GA^gy@;SIwdMiNG*N3+J%$Bun5|8iq|{dl`HO!{GhKQaGx_cy(7=f2y2zw^WY zN6#c@a(XIPrYAf9)8S{^FUqe^)1n!~%#qnuv-NX6bMNLk^Yiol@*i5I6t>5d=I*01%CTVX(4*ECFkUziNz7$kN|90%HERd^YRPqGF*A0q6Xa!1K$W zb;)0MxdT}M0xUY*K<=>YvRxmDxgyWD%K5<@&F<7)uihYvUfgWa0<)sD& z;vF53bpLQ}43CBuQsYxo6H?JsJ~o-_hfj?ca#QL4F%(f^kT99!MP-R-XpVi7S6G;B zAc2wM?{4jonwrXBAgL)-qJNMdKS+q;2$MqtQ|&0|0C$H(3@?g+6?zISEbRTUVev6o zdlGoJV53mDIFUoNmp6vW?;__+*?PAJ4$LyJ5va*gys)6pOaU zFoals2-Ctol;Z9l=xxErllge2A2G&{7w1I?reMSr2Fi~qqWL0|I1F?Mhf7I}B7`_F zQXJT+d=@3qJ}lLaL$c-b@!{+!Y8)+`N44>a3XUS!2Xk#WoB&Lez?MrOF~}TbKop0~ zkR9Y~X!S*oJw<`ul~5 z@dB||m_0v)>@Ko)a6poS-R!;nt%(9EhwkT3BC)NR+`yC+nnMW1mqxZ`df@Q!J|upK zkSqug+1NPJgu%R|u-MRGizxrl7#lBS6w84@z*xHn*#`yV88-1)9!G2qo)Qu~sYwJ5 zCB?=gnHWwE48br1c_AE*V~iakF({cS6h(!3$GFq{kij9G5LS{qEiN{J6wf7MXm&mv zoF7hX<3(DF}Q@_M1mj1)0!Lai>6_HJW@HF1h&|p z#)%0{z~TImspvqv&~WP{M_QaaI#7@h<}ILm;N2YYJOK}Ms2AQdAShHA;>F{TY(#!O zRC=OcsBAPkMA`T8+<6fYV(L_qfwFmR66_#_)DF)>Pr z7Dcf!p$RP8xHx7AIv#upg<&4T7`m7dk4&~^TH`ROZXrCfjk}2FXYEF0Si6P9Vu&FY z7$U=y?G`}5$B8^s9dKx-n+-D-yc?J#c9)kP0D`X4U56G#@Ypk$wgKGxR5Jrhww%hifR9NYLtyw#;Luzan#ow-o)X`n6 zx5UKM%zV{qdo%{?;OOMxiNh1Th~7cLA)yrTKuu>bqhn%OaY+JUvPhhgx+8OER`#x( z+ye&>9WE$5a>_PhM+QTxl05)sEtKAa#uG`%NYmO#9Qa|C?dk|1HaY8}_$d z-GDL-EDzLS>VPXSw_Vb=i%Q7sC;anHc~u3Z7}0J zTk8Uy2b!JdRKV6gLwD}}l20wX-BjHyQz`u9#9oQIIC-kM+w+piG$kiqW9?70(wpc5 z;T4vbPG8NeYPm$QWGx@MI6N*}l|4E=n?Dc8mC2f*0Mv1)sMaYq&bZ<}BCV`^j(VN#IvfKV@|P$r+c~!_l+FRlHphW;Z7mT|4X7 zV>>Zfc%_H6-00Phyl0XAuL>shJUhEI-mQI@rWam(W^)tI_E$(gi@ zv2_y`lck{6g?-USK?6oN8GURUIOSnK4=nj2R9d=cX>*a>y-e)Am7ak0oL{aEyIX%4x!B2Lyd&CR%H zP)W&+cUGLnWpqiD(_w?`n{uzl1d=7PY42y_XKsiJjE@`Em0)A@T5J(8R_wc&)$C6w znc3r+2v=FoJRol@n>v{#$?mb2%>zlC{+sVln2e^vcb*heCu4tpfR~>fPJn+NP#HNS zM1Rk}7r9e%BXUmzg>@<2WcI=zQo_y`WS{UGLMi_ErIgAXlbG6X=hk-domrJ%@-0LY zOMq_`NHEn%u6@Nl>n0+z8dUlsW#-ss752UQCnpyjJoWh(`7Q_k_1CXqQP_!^n(b@L zzCQfwRAvNiZ`Xp7M6NZ6z0MZWib==Wa+lSzflnLq?v!XrO)n1I{MP?CW8CwV{u&PB z<{Mrb$2iGj<!CPu@-JSu9hZ-pqI zD3hr&biYAXkCCimpmdq|UQhR`s&Q>uQ$+nMlyL31seSG7^iMRNX1(qPvAbvS-j_>{ zlcX-)7b`y46WXbhmB@3^7Ojch*i&>S%X_B_kKOuIeRXnd)=$XbLWPfNLLO^ zGIsAdPo>UYANVkkH`?(?*&>14Fv2_9XfDehK#a}<(_6s61#rT%85+9r;gb>@5owf9ZfP}7^M&JRqF zCMH;!runYC81aUH9Uae~L7bQ&OR+f_%f*eGhyoSr<4YB%JJ1)$bf)NA#*Mx_iM_(< z?HD+`EIAICAZyRCCn9!E$D~7NkFWVY0+*6=8yCxN-s|4^a{oi#srrs810p?xk;y24)U|YIm>jsaaH*IQ)MeX`_ zt7>?-M0ta`u0JRC5$EGw(-XZh!~iSj<6ri6Ub`W=Rtj%ak)is`wq43tI^$Y9q1>Za zQ(G|L=u958jBM?i{tz`@KNVD8TPJ)c4n1_?6H?0`F(?^TIxTA%l+0*doI~!J@JvsU zZM&G!-lW`U{6@UAe=6Hpw*T_R*k|nCHxkx_`#b8oX5y*b5&v9sPO0!#ApN4d1xXitEy&-ICQ#D}E1B=F8%!V^GWNH0l^tPhCr%ntdC)>R4W=DkVzOEIX zy=x3zyRUIV&bm#zX}_kE>*L<*`B_cu($|uf-YUfHQuy4RC7<##%w-jWk-090EQyBh z-5&kxQf@tZ%scJTCPK*3D_sFM*lbaCRb7_8Ez6EmEU3jR-*l~M8hvGOdtA0+YRp6W zaeRQVi<@C6L-iZ%YM@I74U|WU@-wfXn>5geXD3gVzayM`kE=tWmlofwi$9&hIeNDH zb3YE)k_4_&hO)I zhz7&C=^S}+=(fwP_&)w;od3#(!e~w+bgf2EK z>gL_js($vcNkFNUG`lpSXFO+5fR<-BTFV}*)Ti@0#((f2;;~D2F5md|aa;NO&qasZ z%}>Z>u`j!@cfBw$^3CgR3S^cIHs>NnBOp0mCtT+xn;J*#V9>e zdZjQXZ9ruiwd&THU-zH+e0=}*&h1QQ{Mg}ZJEpF6o!Md+nJtk9&I2;j?AznJB$e4? zx&x0dAB2 z>B_TtbBc3MdaPg02&ID|vK-f4R-+~_n2|a&jEU^L_?dF!+|X653&Vx}#>FRnz4zy6 z@j^CV8NO|B%s?6>nyAQ^@LXjkuA_C*7XwqRr3%Af=m=NX%dw48!XBZeX(w6fGe#vv z#7b1wxPYIcP(sx#2Ub7X!9QKTKhkaPnFMigKzA%>S}$F#BLg)^z{zc;;*%In{O{mU?Og^Q)-mr_TcPA`tf%Y@I01aZ<)q2vwF$e{)PkdZ z?hn=^up*RSpp`D_FIgIP{0(I+hueMQg*m0j=R2W2x%z=_@eH)OBLmF;W{*albT!%1 z^Y2j2619x>r-KHX;W&}Y8D3I3HLjaeee}Y+O^?>>v7G%wxBkK-k=ZYt^ai1Toqzq@ z!AIb5r-ls^K7FVejkZu(xU{BUt5;pZdb+LtY?Ji51bEHH6xnwdTs#{`QS0W_Hj2wC zv%WmsphDdADC+rFteYc40}vWq&u)EckgfwdrD(3Z_o`WIMUK;xTYc|&EvdY=-W?L@ zzTukg$Fn7eMHWLvV>==?R_<4+E>{k0<~98E@0E|-4@COS7Nc`qAQ|t#Wl1#ZTy*SQ zfAr;kAJ;wefbu0XP3$CtBB}{>F??b9A!RA1U}}h&w#);nI(BxO_KIAvNK3ohB=sBb z?z$bh*p-Hona2&QrISE~a$-x>?l#@4yYZNFTecG-ehRklnzK{bk+`3?6p^_jh3Ff!`oUN0qr!-dUbj$2_TTG_hWe`ZywB8mVEn|WIzJvWF`BEj*WNRta$xeH>Mj?J8J`X-UX@ZTs=+ah zZSv&cg^fdn9f+F!K5yS|ATFEyy8DA^mgfNsWdGrQXV(Mo@0^+>AT-ZLvO-LijU#!p=bqKmL438w{_sRXmeYtA6u zegeA_EDZ-Lc9*P?1@x=12T@yvTQquam)LeWo1Ke`FqC$a`sM)@FAC{p%+4?IcS!ax z+Wxp-;`{u8{RZRYq}iMR9H0eW+JBVlWFXSDXHPntmjJS#Qpuej2dQB_b_Z@EJ9`XW ztm+8EA4t))spl!KJRcvksKvR+{De|yDZ)jqJKd^Irp=O8v?Qjh*LHk(c1|jw>R*WE zhdrrSHhGz$`M}z1?{J6K>*m*LZfHbvFZ{D)QHHMAqknwo+*@$RYRevQT3%4Uw_I4h z@l4f?%W@VbkJ}HB?bgI@eXwTl*zQWr$6#RBP2*=QrG$G=GnX66NE0ZZl6jzid>1d? z{&5m1JD~3RhG`4TKdfkOktWr?6CTIn$U%pOyb8?GJRceA(m-_V8>~uCnS+4p1wnBzacV(ST zsqUmbe**tX-`E26S$)^w{VuP5XqMyCXD({#j#6G5N`Gd9v?A*ud18Ez;Qq>qO|Q4umuIh z1_6~;1R|Z-qqGtb0*H!$Bq|Uggts{7-m}lU=iL9@|Bmr0BP(BORn@9lb5_+iXRXcm zn=D|5gN?ln0D(XNJMaT+PD^^*TUrLXxS?(A9j(C|03d1Sh$E5&b^ri@7$56qYoX@t zkp z97-UDf@QY)934ss-NM}<&PYtaf>_WI#A%5*EE&XuAl8UVAmBjE1+hE<8x#isLXung z@z{_E5bJ_iGS?Z(NlA@Dhap4j1Y6n6Ns_7j)YOH35 zB}ZZ7<8@quLhwPcp=y>SLUa%@2>|{s^HwcDc57_az(I!V9fiYn^pAkU|Bv*4y!nq( z|7WnJ+rO9i;rch7K@?y8mG@WOzw$`s0ARcfj?M3XfTmOc*vb4WPvaT@NS_CQ z#=d`&M{&zuBI4ttkHKJMGWiG&8**f8K>v~cKMVY$3K)Cp7)QjQ?tT`1tmnq zt8EQx2q}t`5UUm!9Tb99)A_GP{J*aFPu=>bejIkghGAo|MDS5wpq1f>;h?&Sp}2S) ziKvDn{&yPwUsn64K5W6i+cgN}Ztwy5z$3tpK6yZJ@f9E>CjkhaECugC{-HNVF)v_i z=3$_p|8Dmn2Jipv`v1BJ;8v58w4oD*9YVL%*^2IPTVfGVI4 z8~}6xeE!#b6><)e4atWTL#{*aKpsFIK{_DMA@3lgkSWL<zbX>?z$WtgpC`O1T zbU~MB_!%M6Zb66J?0@ zi_VI2w@GY+Zqwgpv(0xKaogE#h1>3KYv0zt?en&Eu^nQXV#mbLVxeM5VtHaW#9GAq z#Ae0T#bv~`#7)IL#3RLj6Td88Bi|OXW)4k?N9~km7Ea+kRxb{r1r9^z9|v z8@Kmw|0XRatto9T9Uz@7T_{~A-6y@ULu|+X9hN(ScF=Z|?0B?eWXH0MoQ$3fT81EV zLFTT^bD1x)qO$vCtz|=H&&yWGcFE4j3CgLQ`FbxqIh{ zo!FgOJ8O3i?OfZXw##}Ke%HlaO}joQ3n?E`c2y=Tmn!!tFYK1zeSCMw?yTJpcQf}0 z>^Zc@ZO`dF6?WAELw*KTjZ-s^kc>|Nidwa;_k*?qP9KB$YU8>@$@|DoQg&enixIB8Hd zsx+9IVw%R95t>Dsy_&20wf1B7r|)mt|3z!3mc3T8R+ZNH0jUGX12G564-6g@IcR(k zfAH$Tw}%7{86Ao^RC1_KTRm=$_=}a9_JmPrd z?2)D;-(VUrU)V)hFO08iq#LDsLw8J1R?k82tX_-Wcl|^9A^Iiyg9cItHU@NqW&@6) zwjtKA)bPELoRO1Jx>2Xm1{?v8h1bC65E_V6h(8e{#`4B4#utpA9Th%mag=_v_2{o- z@MH1E9v)jdu5%oJ{O<8DCR!#~lN%;8ru$5TOs|`=%+$U#kIuslbfC!)vecE&OOlmuKS9Ig-4#pnCAh{1kX+{ zX|I!Bcf3|HR+xMY%NypM;{DP`*$3y->?`W)}Ty);5U2H=w#Z-VSg=uivRNf z<$$Pwwm|8?puoCQ!ly8&?w;ZWp@YhUmV@ns{|sh_ScVjZ%!i%`{UdY^Yl_XsehxDY z%Mbe!ZW?|md@ceRQ5dm+v&0qSIFWXdWs$3RH2xNTGYS(`OV~y@MR-J%CE|(QBvlfH z^e$REIxU(Nb1bGHh8>HFt&D@j`NuWK%Y$UD*N0FfrDX)?a zC1oakPPR$Dd0Oan$mve%Ug~eusTA{+>of>0nAS;Gr=O?Kp0Pc1`#165@V~u2t9v&8 z?9X$Ub1mmp&Yw9ylWLnb zdSm(i^1=#{io}XfH@t52-ZZ{>r&75xyK>_e@fPd0+wJZj?)y*|JHP>quYqReI_Y>}aeQ@f*@I%zY&N}0|ntILpKO5v4vKk?cNsa8Lh$dFE zPxHG+4v#upj<+;CKJxfh>)zIqHifplcJcP}?VF5b#`2TsCkq|n9W$MQonu|zU4z}O z-EVqOJ7_b_6I%q%ma>#k;-LU8I`;n6)toNbszl=tWa+rzC^|3SK!sA&Vc6=zD z*fUW+d2q6p1!uKQSxvo~cAp-b37MJy826Dkd;XKur^3(B&v(A)e`%ewnS1-y@9XS* z^!)ll+M>+jpWhCAt6w^?^os4xp5?@HHosr^vFpdJpN2m>mtB@8RtPKWt6AJ#+}pp5 zfAy|m);_P3d7`|_8wWR9_$dDPCSh}Pb4tX~nt}@h04FEl5Xc6$0U{6)KoCR_(31cl zvj2fWW&u$Kxx(K$h8JY_KX3r#z+dIlaepHfTRa48^KS|CU;f5R{{AbJp9YA6q~jKt z`{y;tU#(vg_|KXU@-@N##2^a+lexR4z5Uj&xw(x8F)}FF%gs61BHqTv&JY1dxI4g; zgV7#FXx$*+xcJaG%LoVOa0hqKXb1Ob6d}md-oshnBc5VS2oWc^*uaBrwT%rTF$f<+ z93>JR>=|O{X>RZ39-&7xkG3F_>`AUM5oBDHrKN*qP(0e+(g99FSzDk;F}MgzaZ4*Z zZEIIuQZND&bo40PSlc_8psnp2?~Fo6+a!9ygUQkM@y_0!E(Bv+17{EW2xp3IsJ$*p z&pgJ+JIRtD9_H6q}CXmqtA1`x)x1AR%)H}#K0p=3nmP`qaq!=M$ z9TO9AZq6=5w`iDeLa=W{khhn(yJeEEZoC6r7o|sZ#^}XH>boQ+#`;*f8^DdC4M_-u zo{w&@4c^hk!3l@P#-kF0(GhV$QAT09ak2WwP9fsKR!3ufUBi4_y@TxSFuryeC#+Yv zw!WQJ1S}eFZ>UYNF!vz%7n2U8xbc|;`j;iF3q~3GrA&n5$=WEIP^^ZEJ*caD!po z9mr_+FlToHib9OGbHw9=W82zvk&(D?Baa}j5FF7w zBH6{u!r4KefJuzB42jhCHg>cmdBqctMnuHNxLLrottjG2WEZC-Us8gLF)_vnW{?zt zvhyJ5qS1!F&MuLLNoeCxoQtlZt4mxW$=wi(b@tE?H}na%w$)1r4>I<&@)ajKA&hK2 zUF>kNHb&S4M<-uYILqLm z@03gtkG9j+$J!dk7!s00+=%Ena-uCdDM;5SfIPH5Nl~v~@R((oMv8MLWbfQOLW9R;hTC~yt*tRw-vqda2S(gI*2vhG9PRF446}}QjEFFf!V*0r35YOH zPi%COZfukxA}J}-o#2j5goVJp@g77MM~oW@mKg2eebki<6ORcp@^p#ta0!aA*K=@) zb+oo55D3u}E60$K&{&7?7z20$-oeTi=H%dN5KYvJMMUE5BEy5M!idC#WQPb3a5`I{ zVCHt1xCDH-v8Q`<0vs3Q5R)A0>>caujPRm_1X;Q`!QB&VLPJruB!gsUqE(Q$jk%tl zZbTvlYaJ!-mJl4DY~}799fwa$)_09IiZMubb&RmJb}|Yx#2XNzjJ4hE>Yo4rM}W%N<& zIDEXdyJwWSdvvHd9EG#A^~Sp-lEPuGp~3DJiFk`JQVh(^AvVS)5sx*{bu-Ylhei8} z!>p4-tR0Qr6Dc-{xKM4Bfg!oGC+o$92K(A#;0f^t*q~%9FIOK| zJj%<7oT%-C2zC$;BU?r~AlxzHz~&fWxfQkgk0c-f5fBg(*h<2Jf`UTA!XhHVU=k4( z6BQBJ24Ye1ZQI1e#Kpx$M8ze<#Uwy1w$%t&Z!3Xyg~UXJMa2HE)8-REW*cwq1sZk$0uVt#0U<$QVIj~vhNOV^ z0U;S-*}Zz^B66-lqWfax^?$o~eVe+)gAN6^cWe!V;MlWb;)+T;cPVS`*E(?Ukf9MA zVSMzMrIodft)0DtyN9P226Wp)La|}t5xB^>_=H3?yt2ixxjt&KL`CkLID3oE*VfR0U;qlA<-?lAOhqq!DWPm_v(qrn!Aby#mMc` z|81MR#l`CnI>gis+}H}ivG2qcH4LXTIa{LrO|t))U}yhVlKn%lzvN;9l7b)!kr9*u zkN}^5pgarsx8K?_WCV#xXTcV(PpKfLMHgi_`}#U3gdPtr{=8oGRnK8KvEO-07InpS z7oocAp=k5v8+uDl-%5&(O^TYCQDNL)gqf1OwBpyi5wl&x>FHGSpeinH)oRdiy$erD zy#E?^TGC+uyx&Wo-~V9F>Fei90jCM_n5Sh@jEKNYzUIb5Mg(&7Qg7h)pDM5}z9QTC z+)SYK*EMuT_#n|}cZ%1#cRe&R3+1iI^yK&U73Lh{|JaC&2cXz@*75*mHgIup-$wZ+ z5J7)G&llSSaLVYZ*Ma`%9J;*Rs_bE!3cKe+Lr=lI2hW=~fy()%ib{Ae>a@Q#`JnHH zN9{`}SIgivXTEzAXi(zGA9uMpJHS6oxoBd_o-MUkHs;ApeQvJr*U0pjTP2U=&nv$$ zmTK4W8Yf|`n2@!r)^syu1G#hQ98F{sIQw%G=+LDSs;GzutwUfdsHcfam41ZbrD`s1 z0Npl_aMb-!-f5}3Xd(AzvWJ!D*ldMXKT?b)M%}mZcoV?;F}Mc;FYuwbmZC0(@F9v8 zD|Nk~)HLRBO)0)s)@-0Lf;Q3LRk^hNj!HfA{E_+FR>8nVN_qP(?!Y=8N0$bLM+@_N z1I77Dk)&dS8y@%RA0;jwA%^-hB3kHm=6eomn`F)ME?=At zyc~sO)olWG4Np_o)v5NwG&$ahw|syaIHbvbo!(t5V|inarpo^Gh-9?bHgU1qWbN!p zUw_M(%5lrKpnS2i$g$UE5rQkSS-iwyB&%kn1+#FDl{e35&XQ zL^{T2aPJVYynbMbu&@aisp02HCvq&?ne%xOagWx^kZTvA zyqp^8JH3>21^16Uub9 z3zC`bw~>#;GIsNv*!xpS)x7Az+QY31?3Z0+*?pCD(lXOU_U?8a^Va zmKzRDZ0UPHvl2K!51ssNO{?p9tF>09*@3SJscGp9nsMv7mkf>x^iIbFGxfNdIJ^+qRO&gV0dFdNSj8O8uC^{YEq$mnbT9eW zgOs*SKrB3!@g@BJCh!Eba^+tYD;3<`F&w<-MhOppjcV7=LvW<0Zsl$QQ^(%!AE|E~ ztbg2;0^bBskIqgH5!Di3msZDzT-0=zpB8g?k;Q%iaiwC`?a=F9yyIMKC1rJLxwm6O zdunxMwY$o4%I`hzM1pqagp|=jDF3bQ*ywme`;A#_E;(=Ar1F>9yH9={>t<9Gw_)8J ztl!HyZOc(Dx;fYKwCV1bGD#g`J-x~2Jrh?q?mhMubN1j&{_0}U4*Qe``SWeWLd!ZJEwr$pyWsh2ng(|x(^^8A6xy0X+|c-lIvw|f*umBUHu(ktfz_SS<7 z*|p0}oY8UI8tvAe8-MniHe^_7#~AcX)9d@vsi?es#NUKnYKQOryos+hVp(C}|a+&;h*_Miz=VtRQ z+g@2xy)_@_?cjs+f$f~Plak$Sro#zeC}0PAaKftTW_RvJCa0hIS(05fcID6KhCdwG zMfn(VI5`+)plDJ&!`I}$Fx&QsTd}Ur^WG?<;#myAuXNFcggoglG-yee?gW=Q=Ueaf zJWf)v@dvZv<_pu*TbE3TuIl*9#Y#U4%7LH1_!_(*Q0us|3tkgy9IezSdMHDbBG7fR z^(xOamiagmBO7Sc55K-Lxp!YQ3%U5;$)CjVHy% zbort?1232fbMrW{lif5^ZjR2x^%;h&`5xbR3>lMnaWuI9mEH6(Qv!v@d#i^RbSJ*6 zA2|7D01bO(wu=qzK{C@JIC_j%BaliXBl+NGP;LFExjMev7|OP1#JgH3peOk@Lb%Fb>xQ{^2f-UOyK`OQBr6G+SW5AYwh13$kYq>Aixj7)t$CEC1_mdg6^ zx$%i~34`$Q!A2_0m}dsEg#rqEWx$3Tba#FYbB2!7)+$+O^ew%ZVwg-Tm=;TV4~wsQ zv?%jgyY1&{bLMz;+kNz12J2cG#DuVJMSH=;C!JNg2{dVS$y9324nJaF>h?{!vHiuP z<`g(xqYC-r-opiK$dg028sd@nwR+I9yts|?n?P`1PAU9i;8U6&*J-LxA@a=?<_Mw% z+t%F^_XhD|5Hd-76_c;86B#WGqXh=XE51nCHKxi}&MpUK?0`d`ngRLAu`E zvWNJIl$liW_Zg0GF*W-><|_e^ceMuOF>jy^m_;A9^vZs&%JdS`a;2E_of6KPNH?lK zR$8;7q*RG$Y0jP4aevHK)U@3uREsQpYAB(JD0)m^rzFXOF9(BH7;x;%e~4Z9m&R+X}AM z6Au4)G1-}^eEiav1A_JCtpiigot?+}~+sCYBkrx2KPr# zAx)IsJv^a2m~i}bj@L?PTK}-mqFVm(ki!ql)lV8m&`2e-Q9z2iHASm;iRs4*Txeju zHt5|1>ZQ9ML!~HwuEUG1h)O3)tws|w_1(USe&)7<*-|odEF@=FhD}tE_sGkpGPdXB zdoAb3+_GDfyo6FI%MQioDKmIn>+X9R{5`2NI5&SMsmgf`%Egaff2tk0nJ#Du`H5aM zSU2_N_Xj9)>8ua#-GQUb{dqGV1fPz4EtH5}oh$!Z$h-kBxtyn?@%TaAkx97gu9zQK zs^1iS!L;%VvurUngtG~BA5#KX@U%(A)&!8{y#AclYR!6fqbWCZhjmmD-muO(VFhoB zw5>mX1OBzDvPWBe-2QMMdgTLq6%@C2MTSGH-UNh}HY#qg=}#BK%^NtRF1nJpxzKRS zWoFS1zn3fL4>hh{L==3A4$;@R9G$b9FG%l@&8pKa_`%{OwlmHj$Ib=uR{h|e1_DD~$ zXdX?4-%FQ>hwhnk->7gLjt@*&%R&B$%FzMndR*i z67w{xo?hS9w2&G%jru~55aVgWa;xJrdB^Dr)o-pya{OMK96NX7@a#dI?gN|~ulN1R za)7)}kv<_z^97j@LiGph>e8Yn*yEKERcoj)&+Zae=*1;M$&65HEf zvK#u8b%T{C3Txo$Nm*m3*22^}nhzRqQ(K88e#&rYfQ9M7F^z`;Ejdzyu3uJTpZOoH zKY&0E88;9;d29XqbhTKQ6-x84NW~PkC97M*?QD2pC zzDyh1{?Wssh5Aufau+#1Pq^hxO%8CeW=H++PjlADQ&2GqW@;(bM303Oq!7ET**2NC zIx4=jm=#16HhRH-SIga|mI~OFTUlFqLOeYnSzo_glkQm>GvJF=C2`0rU%B}8B(5#% zb7x;xOFdMoYzms$zMB`0411S)cJldc->=04=G@4l6wm#o33~UF=Z6iV*$-)}ueXd} zXnx}+{}}HeS9o2Nif2PRbiig`#w6XDXY4XTvcG;`>Ka*1OIk9L(zbfHuvq^kDD7#N z>m_F#Oo%-mn3DG<|9Ff}PebpLr#ysL!yjQ5@#M8vqCqP+r^rp+TKvHAV?|9i9QloN zeCkaZiw-@>{ls@t@5UsSY7gA9U#@@ju%TGttTyH5qx=t_lGL+4#qJ$T+wkPNuA9={ z1@2-H0@E2yq(vjGGlnUG;PNQ7MBU5&+%YN5L&Z&(Bo=v>4yV|9m3cPbf1uN@t&OLg zvQvSRie9~32<-n5-nFKbp`Im0x2kVXgCEXJin=7MajHO4IwWf(ZD)0P?u3v>rpTbx zPGEcI8Km+iz`EvpJOasfE936n1fEt0dZhJrDnfTqgILEiiS9BDpBkp{PamH6H8tUn zcxl}+5!h%(8lYbQ{a?^YA~BJjD`wj^uJgBXZF}1#8wQm;8s72nQ;+?LPj?sO+6~92 zeL|QY$iiKs>>5+AiGCeuvNdzUkP5URMxAs<>n?WVy5ob5YgD6ZT$xO}(pP3rbK#rb z?iS6D7-k5nOk#_xc@5!4&&U? z>?V*|dwzM|zv?zl`RpnA=Cd|mJ;c;0m3i^*Rtu0>ZBY4O^y94G-WTA^F=_|ST?nPB zyj`QSbW;2{a;&C~$?TYf{9}z!Jn_y zx|N?X3j>!^osC@jmwvu7eM;;Wol}gQ%BF{utr;@X%D5J|NnTj{mH&%^NJS*;?xZ*a zTQ-`<7h7FN@v!W`PH0-`Hg0;*4f9(ROiwIV&;n05?%n?Q>`TY|`NhUKKb^9%Bh|y? ze0^C#?OE}3pK34?A-7Re51CpzgRB!y@BAR=z#&{nUd^Rivr#tng9&Zh{ST6^wXwej zydP)Uf9^BNX=UJ>eAKMlbFQaNsrSwyd!^5qZRhgJ#OpT!)yU+0F1@o9F~B3MUJ2L0 z6YluWz4|_COHoC@Br#zV>}{_IpMCxEX9X*`wOyq5Mb2EKb<=s!K=L}FO!aBev{r46 zMQHl64q|;*t%=dCP2i;|!ZFL~=%RW<4(jeMwZdrVm6FIPfL9ADCyDk<5m^szF6Sm2 za;s{&aVNPx)gZ;t{LqxP9C)sMNBzSg6BUKwJK@(+?PE5%vo&FM^;I*6(6aiVR`-wZ z-6;82#k}1pWQ14mUUA+iGn3`NZkOYwXm#zUlzAA`Jith z=T?AU;M^wgu(#{7(Kbz=YsF9@Z;gvBf2MiunDs^+t-X2snsg45b-hd$B&tsQCt$>f z(G&CWO6zfUS-0;iv1o)wepltVi5*7!@#(uYh$C@>9-vo-rl(D4f@3ZS(lJpUmUxOo zPc_>?!FMI!(+GL_sJ_3Nb%idPQ#Cy~HsdvbB=qGXC6TOxcJZ+)@OTX6#7$qf?Ng}g z3$Nh%zKKZ)srcYnQ>F5$?lg%c-ccAAvc2Mm*MS{jRJZ&eH;Hd zqpqwYZ?vleap}VsvmI~M-hu7aT=bfEzbZl`)g-b<5C-*4a!Af|gQjGzGK?AG$aMu5 z32NI$={0Uy)jUI*c8~(s_Is^4<~mqEDM}e|Y&`ue%4@D^^u5zvZpzKpbpaD+k=&*L z%o_d50nr6vh2O%fMkAY;6Gf3l_=H<;8h^Al#&+yBuz4sbpL<=?zvfy!_6*^f9TqDL z(42Twt{A(HFP^t<#q;KhaTuNVx#w2Qxt0|tDI|}9&(Oz%Civ>P=A?3>>cRS}+c!+^ zxF_%8omhB$#Bf>rBZF-T1=rLa@yPR&%5>J1vig8}A_KQHiVn=4>e-mL+Q%Pd4_>@N zHMn~t5?=0f>u&dhr6hr|iWlUUJ{)?7Xni%pm6NiXN@rC=8`IMl8yGtx0}i$iP>ndr zUG@X1-zvyDvkMQHV{P)y-87M zSnM}i(BBwh7&nPCHXUDfzxG0_97j4}qs%a6J4ue}TlR!5wp_bsbn+|B&Hg$iY<_(o zGqI_NI=nW{c@;D%)p%7dldvpyVy+$dGJ)jIa_}n}!zM7+CXm69)}bn`AK<2UlpY)g zL%fYS^r_e3KF#dTQQxteo5YnS%Lm%V>G-!PY%e>Ev-I5CckTAJTB;{`7zVG7{^(f z%Im3Bq=ml z{%kU>!%P(XCDGojNiQ_8OQu(Ic&==^bt$gZ6gQLfb1d`cjpkBR=1dy?xORB_>CDPM zeof$nS1R@id#)k7=@6O-w-*e?In6-NsmcyfQHhvE-`ty1Fa1icG#;>?RKFh9x$pLK zmaxig!I``>lMQ{nj7)|iRg)FCheBG3ZemYd8~F8uBE3@3!trV~Y1X(%dtHf4Cn(a3 zjV4RZkE*WzT8Sb(Y&YPYVlO?Z6$qr7bI|Ej%-t_+w94aAu0cm}URHtymT>K6Zkf=? z_G=rTyq}rBJmn6aEXc7)=Nj6McTa5R>P(qxcQ;;mjlYd+-_y|8lAbJ|l3y-zvZCcr zRr8>UwyZNqL>^B;iDh<_tFUedU2j0D(7%^65Oh|pC0<5l6`LF zxZ}PB0&6F@f`R)X=4s1B5eKm{!

rQ{>imOdJ_9LZ)IEl0U1iB5W=>wLeIkm~?Ha ze_Z&i2_5KC4Y z3QK8A+k@rC)%r8n-QxW8$TYY%EQHT^w2^+1rp6>P z81Jfkzbz5V5pqetcS#Z8DpYGpt)60nb%Nrx{%ZX;gYz6ctUVpk%#VNUlB` z;CG`_qB+*W`L`8g;WOAMgYEc{+qG9~khrq*bL*%t;7;##wKm6cCbc)UrZxOF&Nu#n zV|)sH0#ETe&0)l=Qk!CK0B5n^KOcg3?RAkZ;KQqbGT0uI?}?^Irj3o@Tm{ZioyuZ$ zL)YgUw^(iWp6x>2CRRO)`+98TNr3Q19i3H~Y};XKyOPfBm{~fvO55{x6Ns#$|Au_u zBHH!AVzgm#FEzphmO}f1y8GyUD=t*OLpeKR#xHQ9B(HvYY*~A{cEJzXBh9Ru3SSH- zth@0X*dy6g=(PZDxE=f3nPRyJddQ$gW08x!+Y+jD>UDQYE9zo~U9X5ZrkZnylJx^KNYGJlEb|(4 z6KZLTKT&P+QYfZVBUa*mmZ9SVW=6B?TNlx13^vFhb|Jq!p&g;K=0PR%7!`bFhIbO||H!#b;1@m6-}MA^-zLyy z%L@g0C4~EE6F653F5}<%b=78ORJXcELr0=O@2qrEA*iMG&y)VoRqwDqCXMg2QF%7f zp7=iF3bHfnIA%2d{~uYB`g&_KRP{OJ#jERTV90X2iC;>kc|>th&r)VAuF1^LzTCSr zDt-gbI^!e!sp_`hxY~=%kaxA0KKW0#du?R3>+^>K4uQMUO?rnjBdiSMHmVJ#WY$tA zURr#DD}j2%p15*~MBrKCjK&AXPx_5%)EV6y&iA#xUmkS?D~D=$EBI{_;DRjsLfOw# zNF^jY0o>5}fuPp@Wqi3ytWP=Xj{LD?^kNZ5e{!XhgGk>5Lh~{dkJX-Q7hy&yOXZf_ z9rbCu^?t0I9r?iKh=x7P>(i1W<*KD`iC<+Q$y9c7f$=_jW`ePf;=g2wnQ3z;t@BXa zD$RRLrQDwp6$e#|rk(Vs{gEdhI$nCDHdqY{vX$(3r!aKI#~wKMFP8I@{%fd;vJ~Cf2W2Xfy`D4QwJ?w=oh#4V3xUIKv*^F z6LbDuIuG4!w!EVGZ)eH;M}pFnR#%xc&xozn=>$eud^jO|8K@NZ6Ew5fu}M{rJ^S>w ziKW8U(RbwQJE&=|)<>=RS2ih4vtZzL{&cwZvh08J zLI?Pw$1kmw@r``y@%1?VYp5*fd@EDEIZfwUrKacO2bLGnQ!95wu2zlvEQ#RJW)b@Z z#D=JME`=|thiB&YMo;E#0@4iD8M?F~T9`}jf{G(q4=0-x%DP^QL%BBb)yKQa>J4@0 zTH+Ihm?>F1uRoCK)M1L8d+B0QC*vs4Tsy(YE>5ex!Gm#AtG*l?Ukkf~s~G=ad&d_C zyF2c?kduv)Di=W*>^u8har>(0$vq<)b|3||Y} zNvY@wIQ)PkJisPtv^Nc#)9``!+ok1uy&+ z;yO*x|El1EGGU(6>(rr<`Tbx>qihk$LGvYSXO_|frFiOhw>Ei1PuXabbw5p)dg81^ zc7&n|B5=@TLw|Tq{dz%nURe8Q!OYKX!8? zJ)5S??c>X#w+GDe17-~7R*Mt5Wq)O?SAVJ-tf`2GH#!`9`0!vY^_ryVZrlD=#0^}s zX!_5`r**_TM-MODySLa4XIm<#+Rfxd-_E+LaDoL1{FA|UKCleiO+C1Ala7N)m{yid zxg;&UgPZ)(?`v{6bMYg1NS}ZIRFTZDl6M(V$L{pRlpf;h+?k`- z4VQrw8PE9xDH-*1aer5rnd;!rtFpU)T*noDI#7IEJ1H-}PUjDjr1YVed-QkSq!48! zk3c>l@Aoe5o#G-Xeirmv;Yayn-j{saianH8Ipe$i#vV5x(YV^*KkbukF->aO1i~3&U)v#EX?Dny;^8YQ zg;nJguP)odVHNm*v)${q7Tdgs?>B*Rzm&dZcy||cJoAb`K4kH4r)*m%ZU5y<-yHpa E0H^3=VE_OC literal 0 HcmV?d00001 diff --git a/doc/Eqs/compute_fep_vol.tex b/doc/Eqs/compute_fep_vol.tex new file mode 100644 index 0000000000..0301e39788 --- /dev/null +++ b/doc/Eqs/compute_fep_vol.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \Delta_0^1 A = - kT \sum_{i=0}^{n-1} \ln \frac{\left< V \exp \left( - + \frac{U(\lambda_{i+1}) - U(\lambda_i)}{kT} \right) +\right>_{\lambda_i}}{\left< V \right>_{\lambda_i}} \] + +\end{document} diff --git a/doc/Eqs/pair_coul_soft.jpg b/doc/Eqs/pair_coul_soft.jpg new file mode 100644 index 0000000000000000000000000000000000000000..dad9c745ba6bbb555427ca7b6fb448bc2853caed GIT binary patch literal 11309 zcmbVw2V7HIv+oX_08#}N=}nFFKtK=#0wF*MH8e4X03n1Vl!Sz?s3@Q!c*KH;VgW@! z=>pObJ*e0K1q2eif+QA<63E+}^WAgKyZ3kR_ud_Td*{!rS!>PAT5HeD5)hJDT$ask01afw7Z*b3MjOS|E9$;02~Pbo|=04>FWN?|9?Wt#KdF<06_de zY3t~i6e5WCgE)c3NL=OfK&%!;S;b-!t2h}{5X9?NG3igd^$(dp@s3p-O{GPHGOIc# zMpL6#@c@Vqr7~kcEbas1yi{@w3&hVrY?#2Ll0hs0u^KgokOBY_@~eDC3^5MG79f^S z4hnDsu_FM;$dmqoqyB*zF>Fvz0C1xxrX`a}aSYu}#Lc>v_V#wVo-wS17zV@Ck3ggl zlB0Fq=+s04Ee!zvw0X4`pt9;)UC_z4miD%`rdDR4`~RZ3xE}yoM*d-s`s#j(V=xl8 znVYj%EHiQp(QMVBf6>1c_)GG?2mhGQY<0fBe5Z?yi6t--7`m%YCDIe<%w*k^L;^8J z*YrPc;{SEWf2j2jJ+=nK#Kt7Y(7>s1;4UN6NZ@kQqR9+0ou*5s{dX(;zwGu89aiC= z`x*qQmsS8ZycwW0q6Uc1-v=aAe$pg-p_2WxE9g=@OaAsjC<~6RR&t017AqYQTCx8!!Mi0j7WzfB+nT9e_LF1z>?7 zAPm?A5P>*=3M2z8AQRXN0}- zd;)mDBCrI0$fO|(5LL)}hz`UE0)tpV>>y4McZd%p01^h-4Ix2j5GEuOvJX-SDS@1U zT!37K+=SeM^g`}I9z$M0IFJvJFOXki;$re*YGPVq#$x7Tc497K-eN&wkzypVB(Zd{ z{bEPOPKi~DT^DN+>lGUo8x@-s`y}>V91xciR~Oe4Hx;)NcN52ohl|IGCyQr`7l@aN zSBlq(w~G&nKNX)9pA-KnAtj+Ip(|l3;UM8D5iCKJNRr5wI4p5SqFSOwVnE`l1V@4= zu_CD;xls}(xlIx+87fJVWJ%^pmP%fcY?d699F=?{xhN$ir7mS6g^==;3X_VL%8)uN zRW4O8)g$#->Xp=YX=&;8(lF`m(pYJNG($R1`n2?Q>2B#K(r=^%GIBCHGFCDkGT|~b znOvDtnQJm#GEZdQ$t=k#$r{OSlf}wL%cjW|$zGCemmQIPBfA7uhMGXPLxZ64(7n)8 z&^qWKbPD=aPEJl=&R))6jx4uF?v&gOxw~>4xu5bX@>}HH=kpHTn zpkS=9Lm^y&p>R~;szSfQw1Qxb>Kd~(=rz%6a@LfsX<74R&1XefMI%KQ#a)W&ilvH; ziX)11O0r7EN^VL7rEH}#rCUnlO5c@Ll`WOA%2egU%GZ?dDZf{dRxws_SBX~HuX0hP zU*(mmxT=Awn<`OtpXw#mLDe^EQfek@Xtj8?LbY18hibgFDr@0uackLY%hujrJF70P zZmf=0Pf#yXZ%`jo|D~a&;i3_vk*`sw@kHatI?Z)E*2SzVSXaMpbltD@y6fH7Q`Q%+ zZ(aX#gT#g{8~iu0Hk{iqxM5CHP18Y>s9B)dpgFNoY~z-V0UI+mUfg(p<997>EtFQG z)@iMNtvPLV?H$_j+P`UcX@AgB)p61x>-?tEt@BZLt*(o1g6=8Z0bQQnMm1CN~*>3s8YKs-os?6${wSu*Wb&hqLH6IRx$H33QpWCR~U~CTB^w})iB5adw z>uf(D3=z8#XA$FeYIc5hhwbj#OWM2I=h%1J|J-J~jj^p^+k%6s1I6K*!+S>)#~8;; zj<2@sZzpWOuzl7^*J-!Yd8b)tJ!gV*r89Sj!H(!1S9ZK}+3XVUa^2;#tA%T_YqRSQ zw{31&ZaqkGBnnx8eCV#?9_)U`ecD6cgXB@;!9&@gGEhC9lAhk4#h&A6Ei@5*70vTP zcx8DFc*}bSdY|#;`fTw@_G!n6VZ1QMF;l)qzBJ!fEPzF0k7Hl@nfN97b@)s9`}vpo zzYVYq$P5??R1L%jUJG0dat$g9nhf3)%na_sDdKkGuHt@#AVW$*W<$+GvqFc%HiVJG z+QOy7ap70Ozel)7oQQa{(`IMh&ap_7NOt7CT^n{K?7EFt#1rt1yCrvr?7p^JNWc;* z3E!j8QD>ugL^t9|;-}~x(Z5B1h}j-f67w#0du&PUd(w8&angr4=eW|iIkFr144EJA z8DA0qgMy`0QA7zL3H4MN>Tc>SnhK3V8=z~`+4RSWu*AH?*`#erCz5!{-pN-|ASsb4 zZ45OqnYz#1#5};{q&lURr3zR$RwG-PO=I6r+me=__AcEc{c?sx1~H>AQ!jIGCMU}! z>q0gpJ1V;`#~^2a&YL}`J=J@mdntP#pe{eOP2$bnckcG1{@Q zV&~%O66KQgl2^wu$6J2W{jK1)Zzu34?v=tzD^5aBGEdH)@;TLZ+VJ$T)50@xXGY6h z%j(Z=Jez;^M|pJllXE-H)m3O!6juB?Pd@+r0_s9brEz8HMX8Ia7vEmOT^hPP+h{)T`GQ-T-beZ+yJD z`{r1KcSB#JU1MF7QPbIG)#id0NK0A^uQjf9wk@pf@hz`geeDkI%^hYPRh@dBWw+Pf zF6x4I?e7wGr+0tvN$i>HCH21Q!}m@0hxR`k@E>?M=skG%j>nz;A(x@=+2|67H(rSEj!U43u$zVm~}hesbHKEC;s_-Sb_Z(e!+?B`9Nn-+E~+~`xx$}01`eY67v2Tg z^tb#$@*hdXY90cP`3HgZ%O82kpT80%d4M#Sbd-YJv*#gykA7b4KYBv!&x`*D2FzE- za0zrnqgQ`jTs%BH;|WnX-{>gU0GtOBVI4$bCWJ;OGmvmxARX-+&2SA)v?d0-g{64H zf(c}cK$ta?!C+WfrG_%02w&@HLP#_%G2Yjj9f}JgvSI#SR%o<41>=qkOoREmko@Vk z0f`hpSCXBFM`B=XfQLH_i^RlwQE(n`7St}r#t$8rjJ3ho5@TStHrDp(h}f8DcORT( zdI&0(<_`}{NJ;hfb`46UhY`YX_KEQUSOPuG3&yq~+b3b6;c-bpo>cGTz+h{PXA(Oc zg$VGaSbJDlq*k%M5ArZ6O$4`820uA0@XVdMxw+05r_m2OL#mf2p#X`hp|K8P_$@9Xs9(ZE`{Km zicUg6VJ-w1B`B7i9?J5uwo9_M3nwH~ZJ5?kzSbdVs=awU6~nX(@`_1k#IhJsX>Q3d zEDlWwW7C4+HsOrK5GWzs4VE7016E#f0XA%`6*VZFY)%MgT2VcH63PBJ%a83yg!ZgFDga~cZ65387U1d|9~F;E z4#uPgMEhdtI8T2FcoV$gL{Dfuo8{|a8$wD?2nxUugRHE5QE~3ct}a*)TmK-ee+ zq=ZwcwzNQYFolA^p^;b$D=^xFih%j1*kBk*NIQBm8ySG|N`qSa1bJY*;)rCVtv%X; z5g4E7>lF};qlS`0Y35d`HgF%mkVFP1C6#7JO=43+nBLSl51L(Y5G*APV-*qtO(Bqo z7FOx5^l*3pGQoop6wb!s5`EnhTv$N}T!;-el|Ut11R&9&_9TQmITppTv`S;5U9FSj z$@EkYcW5dlCM+Sz+m0E9vnIp_1<=^opcoboX_dfc`XreLklf;^(Uz3t1n)FUwq>+M z06H--Gzx`^3ktF{PjN*{Gv#HNSG@v#wF04W#tPer6dM`-f@AZ6G*<`_anv<9co1nPo?`N zB)X-+NLVI4l}RU<2QXkHguR=et!u26cPz!%obF@pZ_SR6_hzJ_sR%a=)XLi3)1K*t zWV+h-@xVX54H(Bx0CR}FI7A;1Q-+8uLqr3B4j6YN|5R=@h^!Js z4Ae_XT1FNs2MRPR0b&qwaZp`JNeQqPhGc>5fP}K7ik_v5l&U{LT0cq6YH#rc83Wgw zy=wy=^9-${l5=ID>Kg0TZ!j`8*|d2J+{PARXTQx2>F$B@M0*7W1>-`%BApl=6HAIC z$EPrusVsI{`o8@K@(v!#FDNe(;ODPZyTGXVA5Q;Q!T+D^QU>i3 zlaLUXkY2S5BF0)ZTv_6SXtRrpX(g2IJwX>(@=G%Xitt}qWoaZrQVccuX5{mkm+tQjKC0h3bnJI6 zZ(=eHSV}I~bY83g_Qw3h%e zs(k)^9yiTpWH@w?1K382U+ZRrwY1d4KTg2Ddf%zw1upD6C&_OetdRPIm(A8I61Ze~ zUlQaD{3?qZvj}_9UlXrzIdrCI8{epO+WT3lVV>Q@mmuUh7}@l*>6Nl?EqkDwD*t|j z?BzCRisI1?3-d)w+j4r%yNNTZD9*ysY#ZM9@qwH}UCvosOkMGkY^O1gmZjj!og(1< zmziC72wBdv(a`kP>jV9IIyb%xx|enc0l^Y4Vg=gB69FsGNM70O=UToqr>l{N!|y$3 z!^_EIW;ylmdYl?hy&g_c|4_XvVscj>o_W268+xTM-CL=QQ4MU)ek=lbzC{JvY68OS zrtWCPiJVt+colkQ7-wM(`K;ezX0nFDjpx;lnkBp^V84)~zqKm)pueo0+MQ2~Al};z|cu{DJ2yC#RK4a41E^CKRX?DUp1t$laMsHMy=cN1%B z`-8?i{aAF&SDhDD3j-oRLj=rT=~CrkhUPA0@Lq9R=Zcr?CfTIEa|(Rz+6%klAH{1M zmrQH2Jf74qP-`nO4*da>m7UYHdxZ^^+dcy;h1K;VI?t`S(nq>XKIycC6gcUB*dWW# zKFtpkY8kh3NYA<(nk}n7Yzw%r=iQN?wCM1YsbD#6bilZ@_pL?Wmv-~_OhC=w{og)0 z+jN?`4|F-LjOp+qyK~!3=6<~DmVCc?$tqK&lfQFXkB{G1Ck&*L>)7p_ZzABvFo}AN zTvy_BvTA(^zG>s;-9+lr$p!p#s+%|Ocu$Uw-m~xZlS@4n&QVjOJk-qd!rm1JK|UYVhXeiB)SW+Vv1B4N z>N0rRO{VALCa$zD+TB;Lpxwf-y;EKf+%NuleNySfPUx?pMe=eZ zqTf?cQ5C_NoOOb{PoaF<8mh`Ppc}0`C$?TEkvYHPfAm)p3Z07CHF8Y}=+ca$V zY??EjepKmF$vqJuX(oUg__tLEh$28+1boHgyBU5GDxSq2PrUW7@1_}^1z1$OD&`h#U{mXvnp$2`&f5oTUbI}iJh}7p z;8e?(pPr8f>D!0C$@1ULvihATh~Rk|FyDh;|1IMsii0hLk3RwLp@t*6p2T!CCwC=C zaUaH2g-$6Py{doE_5D)ui-1SIE0) z$2ATvG^GY!!R)4L8@GHBn?oMHmKIaF#lPT~qPCzy1V{)4WWG6S`Fw&1;6w|C-Nw80 zgn^H;%|C9KE_6CYn`2U;Gj6R*gIuN35=4lXNPweFTwVqp7863oFYoGqwk)zsZeSBEOmogc5Ua=&HlejXf z^Noc6d8}z+MZZX})43V7yncKo+SEY=9ICIad0p{*{1xaA#R&>Wa_EkZrV#c-Xmokz z)5L+Qyjr*jSle}L`&c<8aq)3vfDhIRCpTs{g$nwK)?9 z7Yp$(W_qVpZ#~XjpTsRHT(RJhi#xw1GSK_^{ho-OYBNg1 zwzG#j`jsY2yZtGzv4`+2I{hNx0KU0sZfVJo{k3=6q=9cTsAcWn&O;T9^~rYH=VV+N z_<=}|c(8GP`|Xe629f3!^o=TauHW?ea&h3ib_T~jdy_zJP}_+=w6}Yjr2#|<7)9c5aScVS%sTLko`cMm$};~PWfEH7tT zEMIWMCrRGv;EVTX>pn7h_FZSoqUJ4w+p0aoDI2E)`<7N11?0@C1B>m;FZdCQN1k@c z3!??9ysty&G;OoR1P8Mac}>pi%3bv+Yr1aU9&913-VUGCJfqhtH&+!bbmh${2W@*P@MM{0Uk^da9Yk+1aLQj zE84#ll=HYe=dJ70Zb8AXi2~rK$-kHTg3(;$x7`w4j{+W$T@P^dYPVl={~%y zp!DscUb;=KJjK)j|DjHKw&4~=+OOov+x4^!$S>h>wVjWT7S1{knrmi{wd>52dHWXk z2#6ZFjuErwI#qjYLOUURhv4>zrYue5`1$sh(cR5Y&1Pc@Lkkc{_brd@rawM|O#SEG z9s5F<2r6mr){@(rQK(~X0=kOC*wH`L3%ia!oyK3Gx`<{adh3zZ8O z{g*GU=nh|JAEj!{t~tW>em;MRvP=qZi!_rC)t#QKqnpLR)Z%=9#ujUo#?N*#d5WBq zbKiM#i?p`otDWx71(~i@;e`=`;0uSYJasY@{22HlckSi&+UCjX87&d8SUY&LB=r1^ zmNS(6ORc#NuIv~8uF1(MbTSfL8^@J#v3+!bJB?F}8&j_9y_R*slltJ)vxK3IItwA! zL;7=gzKRM$3@>C3z2wApc;$RYkgYGoJ^pqYUZKQpneof=a44)cGcE{~oUG2MZ?wuf zJ|B?%C8zOc{nw6=sowy9cQqhnc4%HXXDK1mQv~E*7w9bd38+hq8G$0_;muhs7FWHd zl8tqJOgEczbRetmtNKv)&hKd*6hB27Pak%yUfOWyg}(by>Qj@2?P+Vuc~}mZl{5}I zH&N>kC}qZtWm*zvAGqzz$iGzlZCJB#xP!tta&|~XcA@Uw} zj&LKG+!h_KSX*>78%9ny>Z;)Ctkc?H3R{YuHwZ5MG*_(d$+}_s=0e}w?zO_mCH%_c zZmsS(5wI?M*tyAh@Xqp)OdXR$Z+Q#3Pcq~(X4HkAt-Dp^j%W^?EOy!#|5dXlX}LV% z(1<{4CUdW^OA=Jkw-hgXam2Wdo3hNrTSx)|>nf zBkRcnR@#>OyLn`MlqB+b!8K=FXQ~!`@$M*?5LV{gteE@BBQBQnO>%|GuQ=B}roXJu zgHsj#_F;Js4@A{pjhxEr>I)0>>m0SAYX81oc^by9{c+8D*b4E%WRA0BCbU@o&C#Y# zpfNkYaAARf(7dAJtv(>3ijHrb=)ULodv%l7)@WZ?_d9+PNpqfoIozzEQz2$c5Vhmg>z*|uOp^jy2#zX8~H-H^7!}guI%LtIkDZj-OVAn@FIwi&dWSgS6D?U?J|B$ z-^z@5U=aMo28JWjGpatSC-<{rlFP~^#=hKHGCU#s!r&_KP6R|}nQ)Jm@ra)7g6?`D zrjy_NeSUCsuywFofK)s*r{w(GvAfgj-Ji-Q+)TUorm4Oq(;-iLXU^d+spZQ~rUKM# zkx->^(O4kO&382Cqh56vc7{-yuZk~C#w&8>RguU2o_)8c652uz&OfPtF+V@eHg5Ge zUH&Sox@c*V*T|tC$W{<|jP#sS>>Q^tPJK3RM`#=JJ*v2-9wEiU9o|{hJFzJy_j`jJ zuPcjHN+N@G&fptFz#Nl_HnR?Q;^?_W!;Z1nWt=N5#P2z>%Sz21G}7) zI~CP+t3b2dg=Ty}3x{w=%5u9KTYGdSixyGK6=0G}oH?K|quA-rTk2gTb8_QQ(^7UEuK1*RpA=%OH$t6r{nmu2^R*bdtj-OKfd!Bc;A<_2TptvpOS5spudaPdQ?h#`$GYu?KNR@cTX z4emmra69GlOJqZ35%D?qe$9ws$h+$0MiD>>um?knTP7Wh$CI3cBETm2*V-!b;xAlz z)dyUWL--`Jl)ruO*-5J#!9C`Nher%%qdOX{wb91S@5S$~$b*^Pof#FO0*PCHNJre! zowqR1uoEpOAPsKFE6T`GF;FUjpNW}&c{2om3SvnR?g#;6w+8mrk?HQ)WfSm@Yi3Wq zBYkOi_DJ}{iY32zOjSIUe3`wiAE`QJFA-mVj5URMHGJOkLun#b z7txkn_|=A?(>&g5F4#mG(wRW?zv|0|3hb-1?`dze4KK>unu&S!fHp1sl&|l-+TthHfHS<%#b#AvtrB(0AnNj_<)lV zFC<^+&%qv?s3>$q6XSlU@6vo+cfGcrsiCEp7jbX46-5t=MSdsX4>~z4*XG2_RR}ig z%w4X302U7|g4=ZP#zk4Mmn?M@?Csea2gA*aVYT1OZbQFt(N2*oQBM14 zSM%iZWA4&V0&Bq{c8B05Ux#CSf&0>X7IziAZ{r@m@e)Pg;5U9uk9=0_Q+A+Z3Ule@ zbpPvH&u2PLybL;9O@r}Ki<@{Pp&EVh1m9!;n=c1O5L146Q6Ki8b5n}Ibr?I|rNs{a z?nt>H$TTX-U;Cz|xs@H_H_CmcG9Bdn-miZ@TF$_ISvBO~%E(OPk3Reh7U-=NnM`@! z{R!v($SvH@i%;&n3hsP%>1#dhU03^w&t{iP)3m*7PQQs|5pRtoKmnlu)V7B{IWySJ z^HXpDb6x%{ejj*mB-!au8?WxHNT1K7*6sS_wC>T{CiWR`sy;>^hMg~afirCD${1VP zeyLn_xuakfZ&TPbViLAIy!Z zgSS{MhsVtqpiE&qn<0TqBN5Ej_v6QEniBfJ(-@23=!Z6Ys`tcw6()1s;h!Oyog;c%^`~b zfjfAqa9ISz)&rTym40gx5Cwign6vW^yH-Y)P$%9kSIqm}d;RmAkHaD{r}Xs0$9OmY z9UJj`g_5&HdD_anh5m)SY56Ca+h?`3N4GM{6qG8V#uJ`m2!#9^}_{1(F6$z%c!!XShd2-xU!01%SeEYHBk zCPLTfZXQTYCwZ*VQg(-VPLWk8vehh|Kr2I*ZMz$ z&AI(+jqd?}nKPKutACXJqwPP+NVfpM>L)ZdzyG5w<_Z8bodAGs6aOgFz5xI-#{r;m z;GgJG+FUP*85t=yhK5;LS^IF<*nOJ=`uFtzSmEzA|7-A1-`ltOy}ys0h6^@6nw*@W zu{o%*q+}8~O(Q)eIu@&8@UM&bf86k&y7f=}*c*tA$EIP4(5Fz)D#H;Ipy?*Y;WBU} zq6UumU(N9Uu-QNLVH5s!T|+?r4?duP*#~SLPyhs1UI9Y#l7QfW>(CR}-{;Lo90hFd zyioY3zpi@-L(l(m{ogJE#n7!lIxazDv)DN>SRD&WTG%>m^^Gd3=Y$Q>BCH5Rxk&cE6fKL2n&b( z21|euVPse?>=>*Nb`Dkwy9uj+)xe&>+F>tXL$Gn!ENl_>4fabwP(VsRK|oDFSHMuf zO2ARTTOe2~PR8VFhm zItwBN(Sq@UX@XS20>Ki&TY?V-n+1CX-w4hKE(@*;i3rIHX$Tnz*$R0Gg$Tt8r3z7n zP79R^-4kjQ>JoY*G%Lgu;tNX)?-14(wh{Ie4iiog&JxZOE)l*f+#uX7JR-ax%oY(5 zQ4-M;u@vzT2^UEc$q_j%a!sUKNa7?9OJ0_IB>7x&R&rfRPHK;o zv(y18veX%=a;axh<5J(HrKNSH_e-OtGo;T*S4ekCPf3GYS>(pdg~4r{JlOq)@2vK;g9l zQ&CRQOcA9>Q7lt@syL%0sHCgpsg$f#tW>Kss`N`)P1#Wyt9(lNq4Kcu+BVf~`?q1Y z6>O{CHnQ#4c8%?>+wt4aZg1NDK}ASqk4k__mdbUNZk1(K1yx(sSk(g6TGfdi0z3BX z2;7mg_9 zaUCn2M4d}Iy*g{Udb**y`MOQIpY^usdFmb1tJHhHOL`Y#SL&`?yWZ{=*=@BOzx&$m z!942%*5^GXs^43(^)XkJ;`q-3Zrf-Hd zyKeT*T;AN*Jm0*-oM&Nak!JDGV$o9D@;A$?mSa{5R{mC}t)5#8TRU0PtXr+uZ7ggu zY-(**Z4GSkw)bs6+v(Y1?f$Tvx7W0fw!djV@z_lnm+s zssgnZ>JoY`bSBI&>`+)=xJo!K{4rV-jY8i=|BP^rxEQf;!2Ceofze34NJ`|3D3z$> zsHYeiOf;tMH{stxf4l!1HyRmzEBa@QXUx?YW~_7UrP!so{c#uK7P0o&bJ$Pu_VMT9 zKPT8HoKILxL?o6ZF5{eWr8riSM-n}04Ufc^<2RB+ldB10gx?5Hh;l?cv5TZmqL7AC z^i%RuW>RfZFQzinywmQc!_p(uA7>~)%G4|JF7gTTY^FnIStgi;%BrKtQizmS*?Y22 zWq&&8cJNM)P)=-4NAAwtBe}DO91q>3!l*IS4w@G2IBnsu`{8>>B#z*Z^dB`kdhY0t zW1+{IkE0pLtzuQGES(k>82GkDf)Gy?0Lb+`)76=Y7vNUeLHuaN);A%*7WaW+n7X z5|_xAW-j|&etbpy%I{aWrHQ2@Wlm+)S9e@Jb#?7p+_mBB`>#KwtI-STzi!}eyu0as zv+Wnbu&k)KzvF&!r9dUQaWh zA-kcrVZ?Cz8<#gdZ$01kjrffWjfRZA8#^#I^Dge)=kerm)H^Re?wf2RM*T{!+x`eVr__@|1`CZAgu-4+MGM0{CT zN?GD8=dH-DT>ZN1YyIl})mO|g<^n5?wejur_wC=yf0+H~`04+1icMg1)(XJw;JtOL z_1<5hzdmuYxT4(4yxqKJzBm8<24Q1kV^$=^m4b^00AF8V52Ou<0U|IFKoCMO$dUkH za(}~+W&u-ybcMg_7$}(P-*FUd*FWm#+=vz(mLvwR(+(Uw_Q36reMw6GXo%NTM- zcp45JlpKyt-Aop^(9}@8cTA#XHr~xR1eF%;of?uFqHi4@=Hp?Jkcx^<4N0-IG?GY( zCRt?S6a7-tC?=@Xbn96C=-3$37^Jnii5EKHU|cxLIF3y54oZ$rOZ5xR#G_H+1WO+j z&f7RJDL5m^Qo=VaB+fM0Gc40LI5Z?JH9Q7uigvg3%)ps?q{Lj1 zYkib&W}JUeEHW%!-zYr^m5t3jD1o!e48*#pp@O`~2g8#5(%fA#ElmSrkse7F+3t=w zY#P}Gi46{QLHb%)S$Q7}B6=VVDan2@C~NDiR3CRQ2}}Jray%)))G7#RMF=!ZrWhtt zOo^$6WNa8I9gED+_ev%rv7Xr|(*%^MmA|PKAyq%gGJ`;fHS;Bt6T>A!QRF1gcv33P zG$l1056wheN~kf35}%%M(8q-kmmZYiNlCCWPo;$7Nx_K;eksvLW-hT<&wwn`xD+o} zBZ(k%ibX(1tf#9HHqJDO7-xaC%#O1lJDE8-C1oU9`uLJlT^+656ViQ+@cvc_{#Kr7 zQd(Sq5e{daU>xY;DG?jvm2Q^g7oHNB?BSPvFgPWUWRw*bWaVt)YaAZvn_-!4h>wjW zm?pZRaA-GAJRvzgIMF*SJU+g|Wg+7%Jd9(K$Y{sx zpjhK1B*{I*h-~f@<`Hay_DTp%HzAU;DRHS``q?R=f!+aO60yG6V0S}neqA!%kY zUeT#Oe&G^+`0T(;qFZvNqi4FSH`+Tj(VJqN9d6>49_|(!gtS1V1_hb85EEToDVf2Z z#vcA*q5f8Z_)NTEa)`N=g|7sXf{P{w`jWij@vgo`K}i9rNe8{r&^oosib*syN(k`v z^>NS2OtLZ$4aXCFLSjaLR*Ak!wlVw&~EAYV1hm&Iv^x0 zF+ITyMez>U-l;l4G#mUarQzKE7GmCLyFGGT9{6+dWXi zH7h1C#?92q+Zr7d=kullnuCdV;Rz5h#I14k&=x8sr zkGmfMZ9&NNMrBAud-z)z#Tc7Mqx?dG+zip7&dJ$+&OR0gqmf1dp`k`DVbNhOfo?c- zu%%zHV`8dBg1=LCP*xHNA8+UtZHAOc@ykpjrKG!Lg{B(?>ifAQW79oSQ(Z&dQ(aN< zevW>bVU9>AoTIm!BgM=KW#M9C=xCDZ=%1NI%*=9(%XX4T(sxP<^^En?cg(_OImKtW zg=P7fS~(Kp9b^5?!ZOVq!z`SA;uBCF>8|ls&hb`WD3q5q%G<@**~i?=$1p^~(-7rt z7@FYj6YZGn=IRz0=;iE=N^y3HN%e}ca5OdYB9eSE!>#lKk(ne9Vya^%KE&TB+>nH} z404OhaLtskaEUiU8m7dgrC?*s(SF$}`q^Pv{Q!Oa7>ZR$phd8ken^Ub3@H}nLGezp z_D-{QP7g~CaZ5&dC5NP>1Z7FMCcBZnp$p0+D>=>7B{>coinPKL%meVaRAb+4Coi*@ zZ1Z5NaBDvgGYMd05^&!1Z2c_>2*3mcgakH|kf5NTknrDmm;lr-5m7O52}!6z!&X25CMXDXS6EmGvY=sypyz;)tgzfpV@DDBfM`+8R0WeG zXK#vWIn}f)1`aW`O=HrIic2UdZ`-b-qpP=T_Z~BI3rj0&8)p|+H+K(Dub|)%R48QH z$Hrmf6B2Pr=^5nAEK2slW5-YA<)1uNaPIttizSyXUn#wH`;R+!%kNd(udSDJ-@gC&$zB83e{IqQ$=d%I^uM_Y z{)H}Ch%NykAweP0O}bzLS(}8*3JLEt7Ljud5RFci*EBgIrr>n;W=*@emT4eUF(z$D zLP^_fR)@7o+FvO9?-6$Ne?-~e3Ht|K6M&Q;q^QUW$^r<0&);>c0QlF;joko_j!@sz zRS3Ep9glmzxRZmvc41*qjIVU&P-2@I_{!ucBWT73!VhzwghC@Prdn z)@RlAIN#ZByfOkUZu)SP2&hX}u*1w3VUWlBtH91)^_{JwfXHM?*J5!YBh62WBo4E4w?33UkGn75b zyT1X%`wUgmQzRx|>#0>2mP@$xe@~P$y zq9YGl$+L@Qwo9k@?bv&Nu+UypY5Uo~PPFJoS`kBRfwho{W;QGI1MeYa7iyMG! z)Gnpv9sI7`Mk_tO9FgIZ+rZNt`+i8XiR+pLZ210#ceykSgM<_Y`FU`b=vG`QyyAYSq-df zzTCgVXdpe+qKqWngNieGRMaz%aiR9N2@N_}Qs&uEb6RZi1Z}RZf@2v$DeG#MIh8RW zo9o%ilF4rkz!KEU?{w$LMGd5UJr>wh5P^HJ;Brp)`*yYP?fVh2iPhJs*8EX;?bveL zl+p%}cbRu57sg!Wq`&5OL(6Ze2c3D0caxp2OlQ*?eBosa>w~M~*V>X2R8LU!xc2Ay z;@AzqQy&!E0P@dwGPqav!*7@cV2T*xt?4WoHXb6kB^S>tf$mhh(F4y&XVit@%6ui) zxd(@S>PN~)ydgTgnDd4E=3G(#(^)$dO}tT3FrCndv5!8Z{c=!r`Jy6snK}k%`jJjW zAx3F4x9N(l+nKh3BV6p zSf5i?@pV;cSLBaMvAM@jO6TJY%}`4Up6s$R$_~M=2lc<<*+||Ks2^*5aqrI+vVzdVN%x>6|Y9QcmdXZfvJi7ZzwbX5=KTox+Gl9H&X{y*bjhjsG0gOz*-JPVLme*4B@b!*2SjdO9zd z@Sf__7JPoVAfR_4Pi}I#dhy`DU)9_?@M*;&ipC5peuwH=4Qwj(e*(&|l=Ks^S5TgG zPEb3tM&WABxI*<2u5n8Ss`~BAbs1=NJ#t?*WC_j@#(L;#ROnv3fpPl$wDW!BTz|yu z>*B1c7wJHN)JnEaiw}1HshYK~7=skIU4lz5|J~O5FUzVpefsupufKHqH=N1YJ)elp z3zpe&vQs!rT}-P1phi>M(IsVMPUr^E9{pp|*KaD)Z+iaqB{Oz~$(2}lCh~-AMs#%Z8VT4g-oEkdp*kPJyMv!8Y^vh=->3?Ijp&irppSTL4&^j*Wrq8VA z)79)!tI%Le)b*DWJ-trM__{f3mx<$-QWk&rC?!AW{9~;49mbU)8@VQj_Bopur+L_6 z@m3p!cVz>>4IIZbGZO!yt&?rBqxA6K(8%7w#-fEIC0U#b_Ta1BM;?!o#CgAH8+e7FX76^dmg0HC|}C4 z59$M7eLC)D2K%9=$f{mmXZJXa;vC>NHjN8fPS|U^qF{SBx4vs@fCYZ9B~UMRfda_=NPwE3@_y z5l3IklW{TUA{#E&PbY-$TYX?KKYdL9Ri=on*K-(~p!kixT)~OU6@~v<4BXz%2hEQbvD#m(v*Pe8iNa!jYkbe8fJ7Lr0fncw@sD zSMe){Jun983fJJuWcv782S)g-gCeNx_a--lx%lyXP|HZks{hESYO%c2Z)fm$yho71 z$6CXI9qtR&O|)2q41W;)sT;ln9GgQdf3N0l2gPS2;ry)-2dByWq^X2`naHaeJFk1Q za;dZy*VL3*Wcs?Kkv;iU_i^FNw^$rv?zfi+pItX(uJbLqcHr#%qTN2~7V419j82_= zk%!^&WpZ`X>bKTv5JWV8V|%Vq*UAPyD9+09UvB`7OIjzPuHPK4JlnnjoIu{XN}C^9 z`=9`Omg~n7E#zu3KlQflVajx_bHnGaS-LedhFXmY_a@)@Rz5)`cF!~B*;e{csAU^Wp>N_IN}N@uIF%)`7bfDcCPbqIqE3Hp4$v_ z@yF&-^cfwd(xsW=yg*RIwY9P2$NK~3EtK2H5>;#6tfrhNnk`M=XNL)}@VLe%FP_t_ z!-(Gvk4`gv2PRs)K}Zu8DrM=d7;`MRc-D!rXT{R^DPW}4;7%@@$vEB`G5h4Fw4q~D zE5ow_M|dH*+Z&qeKyT*g%kLd3{3GUVrwBwd zjN;M;Fj@NHcaISzRR}gj9=g964AY)YdOXFMe0|Aw^6lpvG9M>ryFW~G<&b=dr5W0| za>pcM_825~`ik&9RK+($o$th4{rNtt+w>5RkF+UONzmaXN-x{u{Yxdq6LJ{KUydca z%8O=8%_)}&SnPAH!Le_B&|rUmYc6fdmq0?A_WXgxP*c~84FFz#q*NSjk+{%2C>QdQ z-W;11Xk${hd)>48OTl4;A>Wp31&I+eeqTbz1CCFwJ+IV3T`lDREr!-Xx=q12^9MPI zi|pb$-W~b=Z`{vW%de-+P1jE3h#sfKtb%%oF1Q4R)EgzjJ5QBZau6N;0g?&uu;Et8 zn;*t86G)XlA*SyRVeL~xBSS+4wU0Dr#&)x8rX=a$o`mK2^Uuy{fWoZZc|WCK{7I19 zPd#>j&%F?Tg$#ki4!+P15ab=FeSS%mqs=}ZVyvqdgTEo(x${q#&+742i&Qs&vr9`! zy9EEF|EKcL|G9Bn%ro)W5F?M?7nJeRTA@{s*7o-aq^I8tw7g01`QfKE@7+Ra6~BcEF4H2B7q; z;k&W94WJ9LEj&@>)5(kqJIUzVQ@!^mKO0Y|h0h-ODfC2Kv3nV1taQxMvc{Jr(XwYd z;PB+XGXY;1XK0D5Cnpk?&(3ZD6ZF~g>TZ?UrIKSKPSpHn_j!#}9S`niU7Dq@C^HLZ8NHZe)IIqJz>v8W_317fkp}{H z_;h^AQI8kyA(Uz9yi+5Q+r!mDE<6Az^^h(Tx~zrS&We z5&ZWSwiIi%iy;qovekHZAt9?K;pt$)jQ}TEGVNJ%?qBPgHZ|gJ$-^g$PtrFm#50?e3Q;;Wrv%c0ury+Cv7k#*E72M{aEZ zZp|a*Cl?2Z{U$hN6W-k&$1(3W07)>S(?NpywRl!Wn3CD+!7RBZFuwRJ{z`mFW67f% z9lZ)3_fHci&6eYTtbu^YnN%iC}n9;$BX1J@vM~=qKt^h%I;XO1PfY_$bY{kS>0@ zvLZ=24RhcDeZ_#K`})1z!`J)+MoSe6o+VZ;A+9_295%+dafNwhR26D}sqPbKspMHs z8Pa{;5>KoQv1nbStzdJ?tN`^30nPpr79_c*g>}mA$*#TuvEZ#BonyrxK&X=H`$OlE z&uAhbBe>?&joK$H_Y=$HaKg};xwG{wYgfIi65s#7ViDu5zO3}wv14r-Tq7`i4k2Gf zlWoQ7%z-5Lys3!7vdhaiIIi!PYi?&-3|5>{{}}muRa55gm%bAp3?to5UE&jk3P0Wd zy8HTm`whT(KYTZ>6UOgA{J_v+ z`EQ>5_)qOI5uw+(4&WVT-`wcM3OqxCs`WWaZ*ZCHU8MAj)A_5r?Y8vOg_h*Ujb~>w zgG(*fqqM&7oIQL)M*6?A?U%->J94AIEY?AUDm}kVx7hzNbL^C%oz|RctW@I|ns_Ji znKvm_>i#)5FS{VOS1s{PPnsT|Y&GrHV$x+cfTZg2PjlsGw7~QknF0%y;=;Rc7DmlJ zD_O@BhSue|6y!XxNN_FmZ^{dg@r-ZC4%90#&qR@h1R=M;|6I~6<+13?&^QW>fTV<* zUl3bq@$e(fYG*1cCqSA{Svb@0NZh5YwY0q!qi4+?6@Bm5-=pn)Df2f4c}&*WJpEbt z8}<~ms|%@vhcwaIjwzq;;Q>&g7?in_?IyXeTKU0y+1sU5jbXLezj zNYZlIgKS!y;W0huCiim@-As}EKiz5)vJ<{p9B%PDWYIt+Lbg*ZEnxuCM(U?~X`pV? z^3QpKtabBi_xSKny;*)yau`J{<| zpV~KFGX`l)+Y;dlc6uCRu0cJsI4?JL-h29_4f{&@`}Z$!x|IhX-RXMNt=}Bs5;&z0 zK@o6P=@HNz6ot)hT1VpjESZk$Dy&b38Ib*T^x)W$hB7g7Bs_fBPW)z6IA-Ei;a<~r zyA%^o`P=%HH}|}3KT_Q%Gm+4ZsX=s37f-9U0l7PPClLusESXNYXIBBz6&(scEn)Sc3JY}yjR3*sOqaF85W<0>E_A6m`BV%u>3 zYq+YJn)5uOnqw8$Dc0$GBnvEgxmY;_MTh6>(^~M5oXG= zXsWrXoEUtRI9OK>##P54TG~$j4@y?Mk`BN7)@Pe!3ndii!yVebZ6N`c zwk_8x`;6^&JB5X$o; zsP_zA^QxLC>Ixjcl82toAk>VaCV7Ic+s;_c3(f2k@k4&XypE%PYj}%bLrOEJt`y*b zAcpzo*|acU1u{15nSGs0cXBP5cTeDE=`y%fZ|#bNSe!(}WQV$2!f$6?3ZIN$UitHU z)QP|OdP6^wR_r;ZTt{$#lS6BFaL`|H}Pwb!GY;7JfFkAdFAT|DN zDyPbKPCApN8tX3KF>PX3$@uZI0H{_-b&JK$7o-g4tmq>?%I1f$P zIelW30?Z!o6Q{1Xdb2yiESG zx#~5MVaim<Q%kCvDsMpEWHmD8SacIXM2%bxkmog=a^D#xmV%db7oy zBvt7w6bsR9A0M$z-mlQ}=v3UBy;1Ax&yzxn(seqn3?B$zv?<%Wx9^jqOb5LHu9D1G z&b6o?W8e~72@kt(g!ksm+auW7EZK&!J6kmlIT_X-I8@g6IQdnZ`_~$c@o#eskL}LV zRj^-gJ_EN3cKvG>Tn~qam_rGMMw%Ij04*(eZSBpy^ULSHwvIeV{&SMOx}{Ak{BF@5 z!jRtcvhjlZEAeD^ensWF59GIof(`YI*##Pt@aY|wuEkf8K$`YXx9}0IwriQt_F_!h zruX1~)!mR87=Vn?Zx?0WP4b`1bTN4LTMxz?4+*mUKp8e107E-%M2pQ4qVFP92V};V(666X4dBRv12(<) zo|T+`zNB~#Z8v!T0P*n+nfEsO>%I`5AR#C7H>uo{i-N9)qqu&|g|%)OSneK9=8@Z! z{sop<)Xw2nGjqzFF+(}=<%cVzhQh*}dy+5qKCk@4byv9B$LcT2?Tu~5bY?ztNzJ2O%vpj zI0urVL>Q#;rI3-V+`W&OtNCPmWLN3vY3+zG^Y90O_Opg}bU#jM7s`e;Jnb6ZT@u{1 z4)5O7%<-fh{O8d8pdq;qa=INa~P83Cz{eyRjx}7=#eK=RA`ZHC86@f9&J3m)Q(HMEqedlL? zVd2Ty66l~n^2#HRNoOGYdG*6emNH*@sJWpP8f+Wti@@>s?t5cCb=^nnq9QxHN_*TD ze+jeRbWJzyE1H{>B#oENRCg51QMT9rDEY$ar7Mu>(wIBbS9YB=M&61(qHIF66N6%K-{G}xxp;?1k90Nv-ev^-3DbVMr8PDaquS6vf~V9BA-pfN6JUC%1?YHnr*WS ziZx$oE3R@$XegQbwe8M{kKT9?a(kW$yV507^Cl&_2NYy?fTvjH?4aQ`L+&n6<6ABT zxqUL%ibXpTKXPuFf(-K|swp49pSms1ZXsBb`;`cyzR=iTQ@-bkEy-+aNsCgIdWtZ%GuQ&xzGnl0+cEtC7VUadVa z>6UwWuWgC>X_nEwdWxz8z3c}J3JKAhaJ-Bgz^XbDk9&WB!?(>v1bNXa%#GE&aF#BQOOM)B! zQ(wZj=o2cQ@T8-?NtHVQq~f>gWoM3Mt~alwO%B5~1oK(8oetW0_TgXaJzC*2xLp0a zi|p5DTkj3_-}|DhY#9{Uu&}&V_rb17KFSu+|75yj10Ys!%2>xLzAE)ib3%vAk!g{i zh@;TPJCP(A`w+Y|_ps^iQiQ56$$H_@Dx_5WY?L1CuvS`ala}3B{|3-RTG=*TtGpb|38KDLVzbXf zHXKu_VlL8Tf;Ue1T5Yg`&GAsnx5YmGc59wK71|Gfge*YJ+{l`i*Z{ECOy@p5n?6=b zYA1n?_1(>5kfSp+;w`yGW$|8g+?$7X_CmJT10ew!mW(>OyudEtBr|*Um<_b+VV7+qf6~Y01m=S2ak{O9o}SUzqL!KI`E;7 z>`+-f)q=rW4)^Jso%s$8V0v1wI?)Dppty5-{8%rF!3?OL2x1R|h06KbgFoSUZEBD< z@u8kmd4-IRkc_zI9xzh0OcHQazLt|ic;u?xa;|&(OZe}H)-jOHLgY`ue|S4Uz93o^ z?OW+#hsV{=F`(Y#5xy98l)(&KeRtvqzKoO?rN+uEgN*-4U%Pm*AB=78S>!`FlH8Gn z&Mi;NmmVtoP%gMFasT!Y#%%XkH~xbJuFdeX1N=>E5W6vKhB^8m{ocgol$NkQ^QSHO z9~k;|+a$m5V69)9VI|XX{5Wh z)s_teNc1~g<19~W>fMK;cr|Ajtnc%f8*VM(ed3N}bXyCSJRZrqDcCQWf%q_v-WhEX6mkvT_&k@l}YS z(bn7SSkQR}aU8=8T?Kb(f||p8>s)6h{#lgHsP5Z_J{~%IRc9m@D_{Hc{ctO8Ve(m_ zgh@}K%5m3fAJDmyvAh5|pCxz|ZL%PLZfXExlIn)b4tu!fZ|@#Db?-|f+MuN9;pflD zspg|&E^itXkPI{BCSMhWM~~xZhaq!xVy%PTRNQ4aDIdwJvJ*Tsv#Lm;`7xuaX9|(W zvPREs0C9_#(ATEue||BX+wK*0JE=)ur~Syyiyqze*w94Laf})wadn)-#xP6D=2s_d z=R;3$#b7q zxR{ZQ-kL#fLiX&Pu{Um4n0FVFqbPydvX&RNa0HhVJVVfWplBD3>4nTkyLSw{W3BkA9(dJ|JB*;ZqG;e z0855uoy>B+#PrNkvE(a*ABfW%fFQYSRVmD!Sh!>2((#}6a%v9Xqfh;KqKJ72z1!LgYFBiIPA5)u%z?(J%bC?>7FSZ0YX%=Mg=*7K=(+~A$l zpT=JEugjaZ)F-K3J99X+JpMlhE~B`8V&*O#++(1q1ewhgZfP8XDZbl zi9aW^bKjAX@=G>n%Cf2^oMs=<>UIv+e~u@=XW-sGGfKZ52csm#)%;;Vrj&;sQfu~}Xx!(Q}m#KZ9yjoVM3GY~63s(tt=F~5teTX{4 z_G#r@_$Br!l45_%%3O7UO7-cCff~PWD|O9EOIt6c?Hi|MOkN-g7GE9|eLDg|M|Ffm zSt8Z*bWo?aomQZ}tJJ!cFt-6Hfdk#8yte__F>~y-ZuG0~4wlB8{v#!^4WXsHvg#f< zxKpv@>smZt3a9(f3@8kDw-j1?>1C#%L`4n)8CAO z)jX~4x~2+EwqCi&8p9KB$Ut@mxZBQRN`+UBm?@$u*7KBJleUFZht5;HroIKg8XW&J zrNG*2c`v`Vwq2gizER9+__c~DrZN4?`bcX04{)X%eSFGR&CS<|R50&2430#${G3QzeM-L zuVWevmz8IW3o*6%E8!e-YQH~4b=KlGt7JN`iN!cca8T>bVUN9?%{k=sEg~nPQr?_< zmZ5Cw1!AQZ^}Kpm`O6GW3S^Y3Oc(tmO}4lUw))~{V4&qORtWD~BLO zP5Ntf4tv$ytgBwEh!}J9>r(9cncDJ2bI3!Twfur(l|&a*Wf!oNi&_uC3+%F4wsUG@ z#a!ofk>AZG#kMb3nN>!3=cMng(#l5;SH&b`N8Y&@f9X#-vGdO%3+G*J@3ZMT_(?=G zeZscGK@KeD7*cWq_%A?O?3}N)IptxlvBC@TAGlxFF1|;qBJUCkURr1QesV2GzpwGU zb8Z*I1&XuN+r;=U>9woNulc(#u~T?ut-{P-ks0m0#wjr-_1evA&dYq#IDd#8cK-D@ z?qVb9^?*66sHg1+bShJSz|N7`GTT&`n*cG>Im?1JwL}}}z>c{6+v|#B4br-jMeeTn z$JBw0N`_hUUmtKf&tF2NqYCPl_QXOez;N*Q#Yy+&i_58Bz%qGu&n ze(Q}+y>bz=jF^a-%6?!_UaFd^uN@eh#JIR~e*+|+A%EsnDInKjBZ{nTH>P{%K@Xea7vJ1C)D zZQ?AQI^^t1Ob5Zx|Acm8sfTXSt+UP*QcqAs$LIaz41ZC*nQ8GvDvU{o#PDp6ZWFVu z=x+NTi|kd?m$65MWL@sOFG<$i_5PLTD#jGjM)%X=IgE)706K?L$%wZ%ncGEPRRtx3 znEdnhofnVlFA}Dg&v~B7H0Zt1zkIi?3yR~~@{T}(G(!--`mT?S=iUB#D-SMDp?8!t zIcU9^^_0z6i81FmRK~shQdLc$DUP)4_IKXj(Pjp6API08irNR#PL?*EKw#;o>9SNs zFsP@IA^md|4#HiA-1C1M`$}@VYW9QfKVqPLWxkd2;LhU$y~Y9@O799Lt$LI$4B1x( z3G8g%oi=N(3m7`@txp3I_^cxCanQ&_DK-VSN zX0tJU!;ksPKOs@k%d4<60Q|AqgAy1jKozzZWMTp ziSMDwIEdy3=eNVRn%@iZMJl(Ij*Z#)ww|d>xBnwz@KDWfCfQs5?AM{_A7@Pjg7zt#$03O!~4dw3gPu z(DXT(@p%uB#$t4pWVLCs4o4bmjh(pq>-wF0I25{}_riJKRBZGi#g@HKjO~cWzK*RN z)2xwtDY@msFMxZWcRE*bzPK1(U){3`?w08;miS_$d#(EOAlCxiJ=>qu@wGE>n5#pu zZhp*YX)MD>d`KGO5PgtxUL_?qF`kXC8JH0?G-8aaqDSFi!Po5qxxMV2-^C%%BwsFu z@se??2pRO|N2F!ID4F1<8mT*~-29~Z$(5LbZG*(DETX{SKT7QN*CFHKXxf1#dJ}`I zB+q^c-PM2yzsJRF`#}fwUXFFHE=#&g_M}}jo8W3lj`VtQjF{t5tx>Y=tF>pzCkf7M z>8`_wJ6`|g8Nz>aocB8;A1*;v&ea$)}34dnw7E!lTn%Fk1-cH)Kr0eRed$lZw67wP%|I!{1 z-KTp>`%(6g3FE>lfw+8SqF*TPXh13_lB0<~IB*JqH5||Ba?l+4TK$vfJj*Z4rX9*j z`TqVuzs_;LZ{AvRua~=O;t4GsPKKOul^jQ=kb6^+jT literal 0 HcmV?d00001 diff --git a/doc/Eqs/pair_lj_soft.tex b/doc/Eqs/pair_lj_soft.tex new file mode 100644 index 0000000000..e32f11f0aa --- /dev/null +++ b/doc/Eqs/pair_lj_soft.tex @@ -0,0 +1,15 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ +E = \lambda^n 4 \epsilon +\left\{ + \frac{1}{ \left[ \alpha_{\mathrm{LJ}} (1-\lambda)^2 + + \left( \displaystyle\frac{r}{\sigma} \right)^6 \right]^2 } - + \frac{1}{ \alpha_{\mathrm{LJ}} (1-\lambda)^2 + + \left( \displaystyle\frac{r}{\sigma} \right)^6 } +\right\} \qquad r < r_c + \] + +\end{document}