From e7f41758bd839dd3c9e8236c2ad5ba1bfa5a7f74 Mon Sep 17 00:00:00 2001 From: Anusha Salian Date: Sat, 21 Aug 2021 11:12:50 +0530 Subject: [PATCH] corretion based on review --- experiment/simulation/images/eqn3.png | Bin 5128 -> 9287 bytes experiment/simulation/index.html | 6 +++--- experiment/theory.md | 22 ++++++++++++++++++++++ 3 files changed, 25 insertions(+), 3 deletions(-) diff --git a/experiment/simulation/images/eqn3.png b/experiment/simulation/images/eqn3.png index e286fac413b0811d69f7986407dafdae45ea3d4b..d2340e79d1c46812bc2a06dc94d566928f1e7a17 100644 GIT binary patch literal 9287 zcmbW7Wl&sQv+r>auEB%5yAJ~dcL?t8?t@$KK#&9{xCRd{!GZ)bIKhLvPnZGDJa3(I z@B8Jxx9WV@vZ}iF+Pi!8Z~eP#Cu(UZy~28pg@AzYO8G5N2LS<54}RZ`fdoIdeY`@1 zUl4tClmG|~GgL?L0g8j1x*P(+*EDRH6)Jp;>G{^k2LSNDklRkDKF*qo{TbTdcwCc;R z=sGOG4kxL%vo8s$UzEy~O`CbG<6;QV|&a zv&vZz9+H487xBT!nCg+K^dd8}SI*OeiBh(PN;XGQpJD!7Pj}b8r0txGV|(+GP^PsGH7PqjPHXOX_ZUdUJuJ(FbpB-vR$r=rPFUjf1v zxe(}mWCeH9_cJ>QIGwJt()b)6%*U_;2!HQ^&aTB(;~nTlaG7oe<)Mlp4KI{BLrS|38zYDG_d zeBrU0h|~5Blt(@mqam1idh0t4v;n2mE1`<8&6H9d_Q6eu=YrfU?-O>Kl&!v00AX@+ z&Kb#eoM7YLpHa7F`T1G_1s9dLLTii9G-^joLB1VSosaARp=u>*y9jmr4GH*zkf(60RO zhQC^)OEdbtpmY5WC<~p3Y|%&egp^h7n=uZ|aavD^Wc`ExMdA?Z{$W?l(&x*&t51qX zWjVd~6qTtzFxz&B!ak|HRBwE1_UQWkM|NnRMQ*ziDLAyHHKchrO^Th!xlCK3!I`9^ zjP(%jP^fLoaM!V+*yR_dILSJ)D0StjqS?)Cn;wH}B9yD^j52DvOHh1zzYPg}5m>2M zHdDsOXF?F1Vk^|2rY|0xD>5X8qu+*GU8Vx1NTIFJ$2PF|?O0_U%^CYS>K%j_8C~}Z z?Tj-2&Gc9C*&YMmh8mi4S)?sTKx4^8iYnR0<)mh|_btB{~o?*0+f_F<#f8OD(`LnvN%15E?YF{mCg-S&DZ>p@PAg9!Q3xgKp? zJgxDZPPX@USk)0Dm(v2Ci`WTzvw9Uu@6Kv%hfA=xV zp=Z;}k~kG|4;mn3eytD8!f~(&J*|5F%9?hu%+;DgXq#Ph-09F=wfUY{iSkJ{tEDYA zDpg&6!`KJ|wg%q8y;0S4w7YO%NYQLD;wq@+&Ys{(OE&OE1)so9*PI!e)uzG@oF-_q){|<_kp zx7cY;Hn!eM{?R73G8~}72nzx%*ZEqth2J1*Z!2&c@1;F*12+fF!`z$$SDxE}n{qPa zmaQ&v5_`-Tq;FtnUj=1!X=o|boj-=lYr8}l%>56eH6 zZq0gZ+;}|h?_79LKzp7=!;%cfO(Nov)jH~iKT z{65#b{DgC`q5U@{cz5lHJiNDa9GY)nL-u8N@xc<&=9Y)FaQvw&?c&`%7VQdos6Wz* zUYkoEIH2v?&6Mz*oH$p+u=DB&>r);D>(&pdf~63oPRU}XV;2V^4YOf}&FMdbFap`` zDb4mf!23stghxvA6(}EtWg6NyZ>~S>`hs%a%d>y&z@O%E1svvl!5<#*c^6D9%OjUl zyQ19tR}p0JB1nI0e{)G1ypp(ave+M4d{DgjdFSn3KQ2wEAzcq+Wm!dqL_4ZK@ zsWF!&4Wqw_qNF2x$OV>V{CTa9zn8(q)o(R88U$WW+>A0l?qewuf$#0ra=p{vyASu? z85xeX+~ie%lX9JRSS&5fF}TeMJ9@}itPowrqKh7YMUW7wdGuLUIWWsD-(DIfVO}U1 zsO;pwi^`olyk_fDXRz9RlM1o)Jc z`xG^co3W{Q%mY^!RwQXqg3x%uaDF*AVnm;n#GI7Pq$V{%0aFPTB%EyDTlJ1L7FoR*yHH^6veogJo zSri+DFz-;1!5MW1$HLS!MgDS`yOq_~y?}kbqU0Go^(#`MHXZxw=HhpQ%%I=JUhG{Z_q-}W!d#%tmU^BnjPs`ZterIIQ26UZ>A-wBb3<@Ym-T&(&}?dl z=rbTHp0rC1hT1Qg7@l+H?65`o={5pNUJjenX%}_%S2yF7b*}TzeqVNDb1LPbJ9m1U z{=P<+hJ3t1O&e#i#Sd}zPwEs^Il512gjmC=*Tz^1&LzxWP5;KZLkaZ^@^1Ou7&E2o ztUWu+iBB|gg(#lRaI-Jwk7W#9^z2HD@uA2Lwu~Z`TkwYdm7#%8dWC$!BY6pI!j+3N zSV%q-*dXWt9WD$}Lpp~3R9Or9fm?8s@A$FBK+dyVM&;hbubVHo|JGFb`$qWdOqF^d zk*siS1ww&ZOg0%nVih}V)Huc>B$Dx2@~lHH%W3jas$_wozW2Ay`~$bd8f(0wd*HU( zZZ>wIaKS6^;{CaEh4qnPw%^-}j$?nDKmjA<#+6YUPiz05&Tbi%2q*k;742_BWDgk@ z8DWJG&76m0l=yTqO1vs9ek+D|wJVL5$aY=7kHUz(+RG*tM;G6iOWX3Y9#xjNr=JGk zzErP|2mX0_J!OM+IfWy%2Xt4Xc!x2-r0j@G)-~`twun)`zJ`QD{2Y0&EnnbM9l@Wv z(E#lw_j{tQB=C*+OlP#nqu7eEmh%cV)I~`-+^a%u^0a)Sib%C<4d`d@YnNca;hZ!~ zGO1LPDp7ipN0E^f@~5Knz=Asd?#(S8UrdqWx0GwiVcDQpn$y)^Pw_s8k7oYj)mkPu zbY%{y=|1lj0&py0mUeZv{>dwsvxsOna-(x~8JhCF?Ne8y6t$GP;Rk$uo3;$#U$1tz zK`Yd+C5e_3iK01h*6eSfx$tV#Q_|B^GY>*BV^cH2X2O3esct`|wJNi8TP4?=4YD$l zuhu{+*NOra#DH0cW>^4JP3$^a-4&ogVN8)?@trS04oG#r`m-`Q303;bQXc&yrkK*r z+zuW13!*uAx04#4PP1p07C0cU%mZq{P<-1Jr$0vrYTIfJTE?xDOX<}u{NGFmCx)%6 zOJqX;9$+2Ft{ieQ`sdfqAYM`N^(b@hI9F$-SBWQa`I0EYfg!8N9Un9!klS?FGVEh< zTkMNu2;0m@c=D_4Jc1q=q^&l;aSYI!EYDnA){%8VVU7eMw2`h}3I`Zc>V!j$Agi4d ze4QibkGV9-R7JJcwQ;M%rrk#i-?bov#9`8jWY$ipMc zDX#ou`&R~`V3S#M;xmIPkD?n9-}*H3n+HG{>a&o&r=&(T%UsL^s%SG8VriO8BWU0Hw?culHa%hru5b~X}R=^oLt>d<6yQg2+ z(p{5IXbpkMQItjQo&M~yiuq!Z5)?vdvgVQKjTWVWl(#CbV${@Nw!7xRGn*S$oUqIK zMne7!Of%B6VpLXhX6bP*B|0eKqu_>5{0*@q9chOXGABLLm&~?uQRnXW z<4m%vU?vwXB~j2k8PHJc@_77E34_3&w^|iFWt}^Z;nvN2gV8)Mp#kB$>O{bZ*9rVMO z@|2G4%l0zkaHX&Eh}^ts25@dMfzCf_o+*|FtWm@9HsEIfWxmNG%FiQ?RE-bmnsG8Z z4BEkzQ4P1V3N0ZtKCaEF%<kwsTl578mH^7mTmfHKA&F$8o>lrQ|Cmz~JqbCj2&l$ILIZt2BCuIgY7TXmum` znrvHpm7BLJul`#GR>3&d#^gh&_8UY)aPH7xg(-TDbxjP|NTT!%pBg)#NTD8C%c#<+ zmbDc0eJi^pck>fCH^n3wzAcd)%A(n29p9_31gU8!2rzFRaa{f=M%X*5ll>}dQBS0^jNS}( zD-|!p5FUk$sM8d&5QrQ8H@>XK+w;)LL++>l)<)tag1D9onW(l3z-&lCj@B)%?N&`B|lw53%cR9c{vAC3v0wF{ z4Y{->(1n-TJj*Wq1%3~J@}zH<%L%N(rjRpgfoZAsUymp4N*64vNu}#pcXPhaIu~dl z;}B14&8?F`K=_;~20b~sop8O*Lr^~R zVRyx-p9X!P2vB`^wT=@)4SXAJ@uQE95r9)9!z#eYTawZRjY_|*b*d9Qn(R9}0E!{Y zu|%3;QkQcEl4K2Ob#0m#^Fd_^#Tj48m<6<^k7C!D($EU7tU)el-Sjo}Dq6A^3)9ew?lB?gLrod| z=x27XDPldomcN7-4`eG68r5F5TQAymVB2deFGyn0E&|xVFWUtHYwA zU+TppIia$VYPKsmytA(=v>keyGOIn)$Q7E%47^143stu~{VOs_L^EWCN)8h4sysZ` z-f65&@@5IFdp)ciy4hQ|N89~H&*nZ3$r1QgQkP1wLZ5u?@5QmkVdG1;ft6G8Dm4db z?PEJQ4_@vmoegc^x~9I47Rq-i)0b`oSr?FtvCJ4}%-Vb>1aUo)7cb;l=hzk%vZtRX zMDJ2jng%S(Ct@gv%iedZzLjUW+KMTho+niuo*dEsgp@ql7z&Dd(7xbA)bFpP&56^I zm)v$ZYUE7j(F^vfPE!m^P}~7lA{{j9q@s*b9_!H_Iq#)-%ann{Ki?(*tPz+TB+3$ah=p+Sb+ z`d*3;kvOx7$~ffIsOFJ5~Tj(==p85cD*;^-gJ&!lzB`?vI;~M#YXS_ zmnK(b3sh_wYTzomQN@Ji{G%M=53o_B^-Q8C6Le?g|In*q0P(1f{5Kw$!+58XxJ&A8sf8HCS|{G#)*nE2g_Bdl3Equ57(>>#*mlihkjbZ9UEF`?udl zz>KK;*wRoUOJU#-w#vit*MA{nGN3_JvcqxXz-?@cz*#wTsWT_d&jkew%A_K{J%=Y) zieRS>G9f36^{hd23S>vg6>940ZfoslThVx+=bNJN)lF9N_di& z17y923JwK+*&6!!LHl`1R9-;g&tb4#+VEe>EZY@_$uZ;<6muPmmuca!=$8HceNRVU z@{TRMa0oIB5-~X?WylUuQQ+;IQc=kHH*x()?B|{XDGx`-!xWFuU5l4T!-7u}TecSW z%{fxrn3|&dxi;KAmw*CxSNyMnFKM7#hUD=wPF@th4ddm2&9DxS%~XQA-SwTDq8Auh zKSY5#aa!yk-v_KNvL1Rftp)V}-F)_|*(NH2pl~BKZ`?Hmgk46{hW^SdY_%Cn-M>y- zjEj$N?0a+`$EoSxLgnd%>?CO?`S6kDhd=-Al=cWaG2uh)*`>Z1pc*vVD!2$eh=#{P zr#j|(6EZ4d{(PNtk{r{ymu+%sxM?;Lb`fInCG<$uB6$78{NcS}4^qp)`nkVILMyul z6$rBZ@^lf-r`-Fv&}ge}?S-l(^`TIPXLr5v8UJy$IQ)BqMza ze>$;viRB5EbHJcPiu3S!zVGNSS!T*HE#2jAdM|TVt!bqNIx*S2{$bhNdHYLM45#nD ztubtm!(#i=F30TtK<0%4@yqYvllpuN=eE~|FC#plD|kd7%V?iiThY(>ZN~S!@o}h) z%zDqePNe@%XacrPL(ba7o%}wUbRO5#YREkK;&5v8T#ZtebYB03y|9V$Aijwsl z>o;|l{R zPuP(vHoW6m*HD^iXzGQE)G2hh@iY9{M`P?Zej;f&cb?bB3j$vN2Ll5Lqi93qXjMp` zV_TS6SiFM7I9)ML2tnh7^91MOS;!|h<>gFY`l0I=AjmN7j2*)5Xp#lY8n+C`mJ+dw zph{N*WsEw23P%-%j@}W=CiQN^sj^@c)pa|5o*p}zaFGG22>SaVeVmj{@5F}YhTK4l zw<+Vf@1gg?{Gp4C7g6}s_2k2vhfD$!F~4&dd@jYE6^Ejy2y{sV600&K z?xV=W3F$!uywEM=qUYPnBF`brON`mAkA~)nK!bWu+D^3yc|0lN)aX?5(XlZ;hoc0< z8{$VNY+J_ku9LFa6?&Sh1f`zsR~`esi(beYMD20^a*ss7IS^s#0Pa947Np++9@0@0 zTAZX}IG#Mx*BNPaO)g6fm6CgG`53%pr~NO_;-wJyYQVBVq}luNLxsVPf$^>BHXed{ zY~3)fL~=Y5WYXd}%2yL|mO;P}Jnar|O&LLzd(50$AT*z5%grNX&8P5&iW(EK zRxaMakY2m#JwZf$YWDW6cW?xB^W}MaJJo#9Z82j(e|g!Y!(D;lBK!sFr(@%Pv61q@ z%Ch%_kQ?8dJ7NX)u`#sVq3QS2c|cK7(E;zkeCYKA3qu6kUAjE(Ht=$n_J!Qfi(bGSlONW$0Cb0YMpfCv&HItc{uHZFlsCO17GT1oB zGcpr(l9q-@^8TM>l7VgGdGtT|`{Kk!^qQvep0c4_E(v3bB?G72I~lxc=%@ww_w8aD zyU)ed)H>7hnSA5#i*APL#x^NEdNRs{@g;w&QajPX5RS3;_sVn3vF?T@kJ7vT*@MZ< zd740$|^q1A8m5aTK#a{6evB28f(`gD^b zmyzvDeMd9mg``PdzwKmn#oRUJ9noVSbeozHJD`Ha+Q3$Rg0gibxw}uB;Tf-|#0d$$ z&i{oG$bG0xo{+~qM{ddui)D%G&&55(#GbweCiaIsoX6VD94(oLaH)7hzNUq_7GqVA zplI#IQMzvdFX7&%WfBXW64SF`cb#QIx*7_g90MrDvrZ$gq@B!7tY_#9}w<4#vT_eX$y)dXEM6+cq|Z3gnp@(nSXj zD9VvDMQ~ZtqlftSdn>j~Ld%T!3Fqz0ac!ewZm)o;;tb$HL+Va%Tt*`tu6s6APzdp) zA(kKktah|{iQnikRt4KsL05R(io&0zc9R9FhK`Sy`k(#Y`It{8?8xri1bp)2g2?Tc zAQOzJ7v$#y;mB(OW6+gf4pU;vj8f?o@A#TZAp)@K2A>`_X$xhB5Vz51Eql^a6OqI5 zWMH0*Xfd?Wc-pu&!NJG6Meh#>1_m0#pIkI<2Rz3(<4hy8C(}-3eYVjrdySNlT9d2a z=YYMM^AnPgIUcR>LdbK_d3_}P&^_%e`#nkbf50h?lPKy18_^r8N6f#FL#K`b3VV9? z-OJD3-Sl3BrJafTl7xE+c{=zN1|LQM1LgmL#92r@Hfkk;(N^bfD!3Z!Vh?pWVne_% z0<0vFA1h{9$?h3FIy!2}R{)nlxk=ixG5z3H(&y|;@R5l}FNw$$5eR_^ty+GI8l(|TYT>|IacIcgb`+Zs@{Iaz=$jfobS|>fmj$m)Q4|vis2=2$$_6KBA1x} zWlp>%1-rYQ9h3JSt?}(Amjeoi&nn%$tpN3^sWOrImb zPDY24;80FYy0)!s?a+pte)YsJ7M_uYx=uZd%O8>_o-IeqA%BdWJF4%%285V;4x)Ak zT%?+65E6cQLhVOr3bD#NNuaCCIFNq$*6n}R_2+{sT;1GeYKS{oTLT<0sO9gEiGrgF zBm&ICpYFopiWX0FE5asKY#*|lwnPCK`&VoAL+%O>1|azjaF-vYE)IJQhSutCPk@D5X1;Nv_|c%s9AdxwL(!NM5|_u zn577fSRr`)-}n9f-cQf->G^QZx$fV&&vowe;l9p&PNbo}1`|CmJpce;($Z8j0stt$ z7dVgh(nZfb^@DsdQ1}>Wr~;}m{C_SCs#lNo9s>ZiaSUWz>I<9BOViv30ATL^r&08I zmb?T2*t50N9)kmH@Y(qAf;Q%NxR&D2V|STmLB$#3j@2D*I(0%KLX2H&q)19jcWSL6AJ$Q#WaV!by3@*9$;FOTvP$kb9bC;5 zsBGW5#;P1ZDT1ut@x%q%@idZcoX|62PazO@kq!Ur3xql`zZaEP1(;*0Cc*fsh4w8< zLB!w7C4ZVJ=Cb=FcHVmU-jcPsJs+q}Wy7{pAyt4j6qp_Hh6n&1|bWbsPcK7{k0r?`>e&KKdpvCRvsT{eRXG{k}@ZOR4X|>(y z5taehR}2v(SPl68R{w2deZ9vl0L$F5ncJVr(uKbYp9Nd-(`ag&cy1Oha(UB2rjZU) z+awXIOsh0!;YMa_&cULr&#m3q)z&%zPDf;MFuU)orJ%%*>xOAbJv4KLhs0A!=D_p- zw0`8!ZZ7LqA<~%BN5ZlPa!||9i6YtT(awD4^H}`DSS{Vo4D5#X{WX#++E|&GZP;~5 z{&a_T(|Zj4kX()!w<{D7&@P3U37FyGjYrt3DG9wnAS=Fx=F6?$PTSF_t>mp1ygab5 zj--EN)eIZ;Vla3cL#v2lu$n4?ObM7?N6)29792M=#QDz&{e`-P4x@_BPwR_oAm`p(_P1w<2H@I0^>qj_;td0H)c=c`7NI)C+EHU zQ_}`Wy~Y?04L7`RAe~}Tds8dlU`f(`2-5E?tke2cAcYI`eL|)Vh;|#gg!$g#e-=R$ zK$6&Od6;23Si^0^YAnu2`c1hgb8F{2aUlz*u^l@L-R}$}hAxL|rk#Of0Vdy0F8PI- zP`>KM=&b+;zoV9w)`k`HD}1s{tBkG!vt2{$EOoMn}_aEdY~wXZyuv!DioNW5PiU> zVC?iUC9ZX-y_U6vFJ{l4w<*f0S@H?(pNM${JsF3{5*|ORhk{g_6@}h$WA2sDYFMtb zM3qls7Ci=My_1dX>COypFrXvaDJLCIvVn|(1c<7XUn3ucvr|3%C^xJyU*4*PWb?;F zD^7cpMfTMVrH%1ui@N}to^z_*n$YF7bpsP^bt&6AV4Xd%T_^vbh9UTIbB{9?_~D#x z3*nu?-H$&F8wuS?^I6tsjDt=BDG6^}uk4)4eRB_``vA0JI{X~Eo+W#%a`bqT_ri|N zKU)TpoEzDaelC1~w z?dJ9;ZmNsrtmB>?cw$nROVV#xRauH~S?hz{pxoV?kcU_ws-PKMWmBPx^vvs>=Ja$>#7S|zTpb1unXQ_g6CP!N<6#9k-K{| zz3P<}-Vs!2da-`1n6g*(40x7;sK!B@s{Szo*u&Df96z)rwUQr;2&?}DA!-~pl#WXGgK|M(J4l80wUmRQJjv_|& zL5JTE?&Jrfjq)8by}aiZTHV)ma#^iYfJKB|3IAyNXa=$!JkHlT`PV5c32og0(@4$nh3K zuoG@DRu_lSiXVN_j;@7mYP$8WD+E!G*1CIn@3Pt7KH?X+f;xzIBTl3`KA^ACIH}o( z*E<(P1WqqpvS2|5`Z9v1R}%e2*|LWB}E;BDtSz6qtl=4DGgNi4-!mT|27ZwL<|0nnPXDCiLWD-_`{>(7&kUqIrwm^(o zww8_L&^G<8;fKUh_JK6Bb)mHKRwa?hW7mXO(=pq--CP)fl;9r(r^o+78sH}ok6L~w z{Pn0r@PI@a?#r-5Lku1yWrbV34cOj7Vee^)8Rg#=lSc)X2n{nuh}Y_U=aJv#u>)~i z8`1=&{d7yYI()?V#*N;f$4&f-Ldoyd5Is*8TmGWUkp|KG<^4N9S^OwJB{MCp-Noe| zRuTF?+K3eU6>TpyUGd+D;xL2Q$V$WXHjST{x`22l--Rp}C(=AgOQ&=<;&<0>>h4rz zN|SVQ@-$6FGdHRoJJ|6s=Q#N>RphRo$UR)(aEN739iiat@Q#PK0T*IsIZ-(<1%jjP z6mM3fgd45Ni6puda%k zo`cim)wl*RjU1Ul8RgLj(La)r1LfgML)El{iip=Ja3AVacrQ?Bqc}zdvQGeDZ`-{qe5%V5~FErl!+)otVukBa={kyDQuGn;FS30XJtMrTJv|iO-n{*_USNUzW z4UrP?i0MDp&HtgK{*O}`hUDFQNjFXs2adBdk9Kvuu5K?!ZptzVv;_fYS_PwvJk_Zn?u*q1Y#_B%#!!!^FT8j9Yd#}b zkX+SY`oY&;zf=*f8!Z?xbR}s&is7 zSxC#_rcUn|{*L)VB*hb4&T$qNKley$>K%ICSM*JJy%xDj(P=Y7il-4N67qE|^F!kL zX#Ab%3fJBv_wVBw#YQb#=}?6X4!r>M`Z}%q8hvTmNwWXJy$JT=n4T&6Dh!A)nNtAz zlU3;Xli81_Ve3wIWvcncQU3L6F|oLE^*T!sYPk8qFR*qR|FWu5d)$QzT+3eXZu2}D z!yp)7n#012a~7wvZrWU43ZN)l=C4*^ZY83J#(wSH(j4OzUQhRZ2{N0SvNKX+?-%(7?RaK>3M<#oJ5RaQXHeEF4Eh#qJ9kLRC`UZ>$mV3zpvlk z+x71|hlf(mUE**pvcyW5?~8ckPd8hxC0zJivhw}BxkxJRC2E4tm*%FV?^nb(jVqio zJ+Ju*i-(Lk?l<1VZgQ@7rlN0LN4Bqt|Zb8n6eX}TJj3&Dq%_OKx$;z8%7ZKzQ zRL%^H<67#ntoD};XAh+@uGJ(80FdFLyeL#519a*CyTCs|y8hv`sriKGHo3b+o9QTZ z#K6Itd^Tf?R`6>Yd4S(lUz|IfnNK?ii7Qx)(kJv{*A(RzD7JB=)ga_D-6K7s(s#{M zKI~!eHH@Nn>}!lMUBD-%xYKOMN8l6Tea|bP9u#BG`G6aII9IOQ?&t@5&N$BcyV^SS zjF$9Su#nfV=hvzHn)X$n$1#wbde7SoU@oMLs~ZUZjDz~2#@xT2PtmIT6F_|Ovfk?YDhf!Pi zU)H931ocawlVz$s;1x0PDM@Ny`<__}Nv>IUgNJDKM@$H=%5TLM>Lo$NpY{$S>UUUT z>*-{c3ZTK3vo|E#->sOv-SjZEXHSKQD zO*NoEqnnU^Tr%@gleG<5I_8tL%zN&TH`yT~%9<#^xf^xpBQYxm1W2 zv_4%Vi3dD5Y3cH56t^-c)YIw9T9y36Vb%n%Z{x&E(-{c0%IaR<=W(!Un~OCCdM_ws zX?xge$n^ssqT-Q3PkU(6ct>nVkT9NXRELxI9pJN#$Z^wX z=gG6l>Yod9Zrq`9dogY8W4R74G1%&@S9qCuD=$Ak^TB7WOl?3e1?D4axH>tey$hT( zPI_wWp%N60GVAJ6A#<-%6O0WCFCH743)8{TN2j=mWR+YsK0|B7mglohp}*qJH`uM- zr}aR9z37jqwj>Q{YL~tmHy-Z<&;}@r!QM2^(R~-Wnn@F&jGvuSxSX~)-gjpG`EqwQ zb=Vt)@T0i`3c$i0edrnufS={xi^Kpb^qgi_Q>A(0hWzb|-#dVoy1rVK>WkO^0xkj= APyhe` diff --git a/experiment/simulation/index.html b/experiment/simulation/index.html index a2e0aa0..7f7c1ff 100644 --- a/experiment/simulation/index.html +++ b/experiment/simulation/index.html @@ -228,7 +228,7 @@

   


- + @@ -386,7 +386,7 @@

   


- + @@ -483,7 +483,7 @@

   


- + diff --git a/experiment/theory.md b/experiment/theory.md index 51f71d8..cef27f5 100644 --- a/experiment/theory.md +++ b/experiment/theory.md @@ -8,5 +8,27 @@

Alkalinity of water is the capacity of water to neutralize acid. It is usually expressed as Total Alkalinity or Caustic Alkalinity in water. It is significant in many uses and treatments of natural waters and wastewaters. Alkalinity is measured titrimetrically by titrating against Dilute Sulphuric Acid. Phenolphthalein and Methyl Orange are used as indicator to indicate pH 8.3 and pH 4.3. Phenolphthalein process a pink colour when pH is above 8.3 and colourless when pH is below 8.3.

+

Natural water alkalinity is caused primarily by the presence of weak acid salts, though strong bases (i.e. OH- ) may also contribute in extreme environments. Bicarbonates are the most common type of alkalinity found in natural waters, and they are formed by the partitioning of CO2 from the atmosphere and the weathering of carbonate minerals in rocks and soil. Other salts of weak acids, such as borate, silicates, ammonia, phosphates, and organic bases from natural organic matter, may be present in small amounts. Alkalinity is frequently identified as mg/L CaCO3 because the majority of alkalinity is derived from the weathering of carbonate minerals.

+ +

Titration with standardized acid determines the total amount of hydroxyl ions in a solution. This is a well-known water-analysis procedure for estimating the concentrations of hydroxyl, carbonate ion, and bicarbonate ions. This titration has two pH endpoints, P and M, which correspond to the phenolphthalein and methyl orange indicators.

+ +

As previously stated, alkalinity in natural waters is primarily caused by carbonate species, and the following chemical equilibria are established in waters. +

+ +

CO2 + H2O <=> H2CO3*

+

H2CO3 <=> HCO3- + H+

+

HCO3- <=> CO32- + H+

+ +

where H2CO3* represents the total concentration of dissolved CO2 and H2CO3. The first chemical equation represents the equilibrium of CO2 in the atmosphere with dissolved CO2 in the water. The equilibrium constant, Henry’s Law, for this reaction is

+ +

+ +

The equilibrium relationships for the last two reactions may be expressed as

+ +

+ +
+
+ #### Relevant Indian Standard for Alkalinity Test : 1. IS 3025-23 (Part 23) - 1986: Methods of Sampling and Test (physical and chemical) for Water and Wastewater, Alkalinity, First Revision.