{EpotPL0.5elTh.PDE  - Electric POTential  PLANAR ELECTRODES }
 {electrode boundary Height He=0 D.Bakewell 17:30 Tu/6/2/2001}
title 'EPOT_PL_0.5EL for Thesis'
SELECT
  regrid=on  {errlim=8e-5} {enable adaptive grid and control error}
COORDINATES 
  cartesian(x,y)
VARIABLES
  Phi   	{Electric potential}  Ex   {Flux in X direction}  Ey	{Flux in X direction}
  dxE2   {dy(E^2)}  dyE2   {dy(E^2)}  EMod  LMdxE2 ! LMdyE2
DEFINITIONS
  d=10   {electrode & gap}  H=10 {Height of coverslip}
  a=0.1  a2=0.2  b=a+H   	{rectangular boundary vertical origin}
  d12=d/2 xc=d/2 Vo=1.0
   xh=pi*x/(2*d)+(pi/4)  yh=pi*y/(2*d) { h = 'hat' } 
 Exi=(2.*Vo/(pi*d))*(ARCTAN(sin(xh)/sinh(yh))-ARCTAN(cos(xh)/sinh(yh)))
 Eyi=(Vo/(pi*d))*(LN(cosh(yh)+cos(xh))-LN(cosh(yh)-cos(xh))+
  LN(cosh(yh)+sin(xh))-LN(cosh(yh)-sin(xh)))
 Dpos=cosh(2*yh)+cos(2*xh)  Dneg=cosh(2*yh)-cos(2*xh)
 Exxi=2.*Vo*sinh(yh)/(d^2)*(cos(xh)/Dneg+sin(xh)/Dpos)
 Exyi=2.*Vo*cosh(yh)/(d^2)*(cos(xh)/Dpos-sin(xh)/Dneg)  
 yhs=pi*(2*H-y)/(2*d)
 ExH=(2.*Vo/(pi*d))*(ARCTAN(sin(xh)/sinh(yhs))-ARCTAN(cos(xh)/sinh(yhs)))
 EyH=-(Vo/(pi*d))*(LN(cosh(yhs)+cos(xh))-LN(cosh(yhs)-cos(xh))+
  LN(cosh(yhs)+sin(xh))-LN(cosh(yhs)-sin(xh))) 
 DposH=cosh(2*yhs)+cos(2*xh)  DnegH=cosh(2*yhs)-cos(2*xh)
 ExxH=2.*Vo*sinh(yhs)/(d^2)*(cos(xh)/DnegH+sin(xh)/DposH)
 ExyH=-2.*Vo*cosh(yhs)/(d^2)*(cos(xh)/DposH-sin(xh)/DnegH)  
	{ E field compnts fr 'SQUARE' potntl }
 ShCo=((sinh(yh))^2)+((cos(xh))^2)  ShSi=((sinh(yh))^2)+((sin(xh))^2) 
 Vp4=Vo*pi/(4.*(d^2))
 ExSqi=(Vo/(2.*d))*sinh(yh)*((sin(xh)/ShCo)-(cos(xh)/ShSi))
 EySqi=(Vo/(2.*d))*cosh(yh)*((sin(xh)/ShSi)+(cos(xh)/ShCo))
 ExxSqi1=sin(xh)*((cosh(yh))^2+(cos(xh))^2)/(ShSi^2)
 ExxSqi2=cos(xh)*((cosh(yh))^2+(sin(xh))^2)/(ShCo^2)
 ExxSqi=Vp4*sinh(yh)*(ExxSqi1+ExxSqi2)
 ExySqi1=cos(xh)*((sinh(yh))^2-(sin(xh))^2)/(ShSi^2)
 ExySqi2=sin(xh)*((cos(xh))^2-(sinh(yh))^2)/(ShCo^2)
 ExySqi=Vp4*cosh(yh)*(ExySqi1+ExySqi2)
 ShCoH=(sinh(yhs))^2+(Cos(xh))^2  ShSiH=(sinh(yhs))^2+(sin(xh))^2 
 ExSqH=(Vo/(2.*d))*sinh(yhs)*((sin(xh)/ShCoH)-(cos(xh)/ShSiH))
 EySqH=(-Vo/(2.*d))*cosh(yhs)*((sin(xh)/ShSiH)+(cos(xh)/ShCoH))
 ExxSqH1=sin(xh)*((cosh(yhs))^2+(cos(xh))^2)/(ShSiH^2)
 ExxSqH2=cos(xh)*((cosh(yhs))^2+(sin(xh))^2)/(ShCoH^2)
 ExxSqH=Vp4*sinh(yhs)*(ExxSqH1+ExxSqH2)
 ExySqH1=cos(xh)*((sinh(yhs))^2-(sin(xh))^2)/(ShSiH^2)
 ExySqH2=sin(xh)*((cos(xh))^2-(sinh(yhs))^2)/(ShCoH^2)
 ExySqH=Vp4*cosh(yhs)*(ExySqH1+ExySqH2)
 alph=0.78
 Ext=alph*(Exi+ExH)+(1.-alph)*(ExSqi+ExSqH)
 Eyt=alph*(Eyi+EyH)+(1.-alph)*(EySqi+EySqH)
 Exxt=alph*(Exxi+ExxH)+(1-alph)*(ExxSqi+ExxSqH)
 Exyt=alph*(Exyi+ExyH)+(1-alph)*(ExySqi+ExySqH)
 Eyxt=Exyt  Eyxi=Exyi Eyyi=-Exxi Eyyt=-Exxt  E2t=Ext*Ext+Eyt*Eyt 
 dxE2t=2*(Ext*Exxt+Eyt*Eyxt)  dyE2t=2*(Ext*Exyt+Eyt*Eyyt)
 dxE2i=2*(Exi*Exxi+Eyi*Eyxi)  dyE2i=2*(Exi*Exyi+Eyi*Eyyi)
 LdyE2t=LOG10(-dyE2t) LdyE2i=LOG10(-dyE2i)
 EiMod=SQRT(Exi^2+Eyi^2) EtMod=SQRT(Ext^2+Eyt^2) 
EQUATIONS
 div[grad(Phi)]=0  		 {2D Laplace's equation }
 dx(Phi)=-Ex		 {for monitoring Electric field in X direction}
 dy(Phi)=-Ey		 {for monitoring Electric field in Y direction}
 dx(Ex*Ex + Ey*Ey)=dxE2  LMdxE2=LOG10(ABS(dxE2)+1e-16)
 dy(Ex*Ex + Ey*Ey)=dyE2  !LMdyE2=LOG10(ABS(dyE2))
 EMod=SQRT(Ex^2+Ey^2) {LE2=LOG10(Ex^2+Ey^2+0.01)}
BOUNDARIES
 Region 1     
 start (xc-d12,a) Value(Phi)=Vo  line to (xc,a)  Neumann(Phi)=0 line to (xc+d12,a) 
 Value(Phi)=0  line to (xc+d12,b)  Neumann(Phi)=0 line to (xc-d12,b)
 Neumann(Phi)=0 line to finish 
FEATURE
start (4.95,0.2) line to (5.05,0.2) start (4.9,0.3) line to (5.1,0.3)
start (4.75,0.6) line to (5.25,0.6) start (4,1) line to (6,1)
MONITORS for cycle=10 contour(Phi)
 {contour(Ex) contour(Exi) contour(ExH) contour(ExSqi) contour(ExSqH) contour(Ext)}
 {contour(Ey) contour(Eyi) contour(EyH) contour(EySqi) contour(EySqH) contour(Eyt)}
 {elevation(Ex) from (xc-d12,a) to (xc+d12,a)  elevation(Exi) from (xc-d12,a) to (xc+d12,a)}
 {elevation(Ext) from (xc-d12,a) to (xc+d12,a) elevation(Ey) from (xc-d12,a) to (xc+d12,a)}
 {elevation(Eyi) from (xc-d12,a) to (xc+d12,a) elevation(Eyt) from (xc-d12,a) to (xc+d12,a)}
 {contour(Ex^2+Ey^2) contour(EMod) contour(EiMod) contour(EtMod)}
 {contour(dxE2) contour(dxE2i) contour(dxE2t)} elevation(dxE2) from (xc-d12,a2) to (xc+d12,a2)
 elevation(dxE2i) from (xc-d12,a2) to (xc+d12,a2) elevation(dxE2t) from (xc-d12,a2) to (xc+d12,a2)
 {contour(dyE2) contour(dyE2i) contour(dyE2t)} elevation(dyE2) from (xc-d12,a2) to (xc+d12,a2)
 elevation(dyE2i) from (xc-d12,a2) to (xc+d12,a2) elevation(dyE2t) from (xc-d12,a2) to (xc+d12,a2)
 {contour(LMdxE2)} elevation(LdyE2t-LdyE2i) from  (xc,a) to (xc,b) report (alph)
 !elevation(LMdyE2) from (xc,a) to (xc,b)
 {ELEVATION views in Y direction} elevation(dxE2) from (xc-0.1,a2) to (xc-0.1,H)
 elevation(dxE2i) from (xc-0.1,a2) to (xc-0.1,H) elevation(dxE2t)  from (xc-0.1,a2) to (xc-0.1,H)
 elevation(dyE2) from (xc-0.1,a2) to (xc-0.1,H)
 elevation(dyE2i) from (xc-0.1,a2) to (xc-0.1,H) elevation(dyE2t)  from (xc-0.1,a2) to (xc-0.1,H)
 PLOTS  contour(Phi)
 {contour(Ex) contour(Exi) contour(ExH) contour(ExSqi) contour(ExSqH) contour(Ext)}
 {contour(Ey) contour(Eyi) contour(EyH) contour(EySqi) contour(EySqH) contour(Eyt)}
 {elevation(Ex) from (xc-d12,a) to (xc+d12,a)  elevation(Exi) from (xc-d12,a) to (xc+d12,a)}
 {elevation(Ext) from (xc-d12,a) to (xc+d12,a) elevation(Ey) from (xc-d12,a) to (xc+d12,a)}
 {elevation(Eyi) from (xc-d12,a) to (xc+d12,a) elevation(Eyt) from (xc-d12,a) to (xc+d12,a)}
 {contour(Ex^2+Ey^2) contour(EMod)contour(EiMod) contour(EtMod)}
 {contour(dxE2)  contour(dxE2i) contour(dxE2t)} elevation(dxE2) from (xc-d12,a2) to (xc+d12,a2)
	{export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dxE2.dat"}
 elevation(dxE2i) from (xc-d12,a2) to (xc+d12,a2)
	!export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dxE2i.dat"
 elevation(dxE2t) from (xc-d12,a2) to (xc+d12,a2)
	!export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dxE2t.dat"
 {contour(dyE2) contour(dyE2i) contour(dyE2t)} elevation(dyE2) from (xc-d12,a2) to (xc+d12,a2)
	{export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dyE2.dat"}
 elevation(dyE2i) from (xc-d12,a2) to (xc+d12,a2) 
	!export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dyE2i.dat"
 elevation(dyE2t) from (xc-d12,a2) to (xc+d12,a2)
	!export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dyE2t.dat"
 {contour(LMdxE2)} elevation(LdyE2t-LdyE2i) from  (xc,a) to (xc,b) report (alph)
 !elevation(LMdyE2) from (xc,a) to (xc,b)
 {transfer(Phi) file="c:\windows\desktop\PhiPLTrns.dat"}
 elevation(dxE2) from (xc-0.1,a2) to (xc-0.1,H)
 elevation(dxE2i) from (xc-0.1,a2) to (xc-0.1,H)
	 export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dxE2iy.dat"
 elevation(dxE2t)  from (xc-0.1,a2) to (xc-0.1,H)
 	export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dxE2ty.dat"
 elevation(dyE2) from (xc-0.1,a2) to (xc-0.1,H) elevation(dyE2i) from (xc-0.1,a2) to (xc-0.1,H)
 	export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dyE2iy.dat"
 elevation(dyE2t)  from (xc-0.1,a2) to (xc-0.1,H)
 	export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\dyE2ty.dat"
END  8745